NOTE: This is based on what seems to be Goku and Vegeta's official fate, as it were, from what someone has translated from DBO (Dragonball Online, an MMORPG that's I guess being tested in Korea or something?). Some regard what's in DBO as canon, as Toriyama seems to have had a hand in quite a bit of it (certainly more than DBGT). The translation provided by one person says that one year, Goku disappears (as does Vegeta); they seem to sense their upcoming deaths, and leave to have an epic battle (seems a fitting end, for those two). Toriyama has stated elsewhere that Saiyajin have about the same lifespan as humans; that they stay in their prime for longer but then age very suddenly and rapidly.
This story is based on these two pieces of information. I hope you like it!
Oh yeah, and feel free to read too much into it. In my head there is way more symbolism than there probably oughtta be. XD
See here for the DBO stuff: daizex . fanboyreview . net / viewtopic . php ? f=7&t=14963 (remove spaces)

...

Dusk.

It was dusk today; dusk for both of them.

The world was quiet and the dawn would be ugly, violent in a way that neither of them knew and unyielding in a way that neither of them could bear to relent—but they would have to, if dawn came.

He could get by, maybe—and braced himself for it, if he had to. His hair was more salt and less pepper than he'd liked, was more every day, and if this didn't go through—well—he'd flicker out as the sun came up, in a way that was everything that he wasn't.

The other man's reaction to his slightly color-drained hair was not surprising; they had not seen each other for weeks, and that was all it had taken for the grays to settle in.

"It's all..." he muttered, fingers filtering through it as he examined it. "Whoa."

The prince closed his eyes, feeling the roots of his hair pull at his scalp as his hairs were tugged at.

They met regularly, but exchanged few words, and Vegeta found that it was not unlike what the human men did. One day, they had rested by a stream, strings attached to sticks bobbing in the water as they partook of a less active form of fishing than the other Saiyajin usually preferred. The grass was soft and as he rested in it so comfortably he marveled at the fact that he had found a home; or at least, more of a home than he had ever expected to find. The influence of the other Saiyajin seemed to have invoked in him a calm quiet, an imitation of the water as it bubbled on its way, the path of least resistance for once in his life. And as they had rested, two others emerged from an unseen path in the woods, box of fishing equipment in hand. "Bit windy," one grunted.

"Sure is," said the other, pinning the hat more tightly over his stark white hair as the breeze picked up. They nodded at the two Saiyajin as they passed and set up their own supplies farther down the stream. Goku had been asleep by then, but Vegeta watched them—quiet, just sitting together and waiting for fish to bite. He never saw it happen.

He had not known many in his life who had grown old before dying—but surely there were too few streams in the universe for all old men to die beside them.

"When did it get so gray?" Goku murmured, and they were at the stream again, his toes wiggling in the chilly water. He reached his hand up to his own locks subconsciously, as if he could feel their color.

"Week or so ago," Vegeta mumbled. He finally opened his eyes again, rubbing one hand across the stubble on his chin. His whole life he had hardly grown any facial hair, but now that the hair on his head was dying out, it seemed to poke through all over his chin and face, the same pepper gray, in that same stubborn way as all Saiyajin hair. He knew that Goku's quiet, reflective eyes knew what it meant.

They had crossed paths more, as time passed—after a long period of seeing each other perhaps once every other year, they seemed to wind up in the same place more often, and if Goku's usual means of arriving were any indication, not by accident. Vegeta wondered if it was some Saiyajin thing, their apparent ability to read each other so well after being in one another's presence—or if it was a side effect of their occasional sparring matches—or if it was the sort of thing that happened to everyone, with at least one person, at least one time.

"So this is it, huh?" Goku finally spoke again. He hung his head a little, giving Vegeta a sidelong glance and a halfhearted smile.

"What?" he wanted to see if Goku really knew, and closed his eyes again.

"We're dying."

"We're getting old, Kakarrot."

"You got gray hair so fast."

"I can feel my body slowing down."

"I know."

Vegeta narrowed his eyes a little, giving Goku a confused stare. "You're not this old, yet—you aren't—your body shouldn't be—"

"Naw, not yet," he swirled his fingers through the stream. "But I know yours is."

He bit his lip. Was it so obvious? Or maybe it was part of that strange way Goku seemed to know things without asking.

"It's gotta be pretty awful. Or maybe it ain't yet, but I bet it will be..." he trailed off.

Vegeta nodded, swallowing. "Not yet." He glanced down the stream. There used to be an old, gnarled tree downstream from where they sat—but no, there it was, right behind them; they had simply moved farther down the river over time. He wasn't sure how long he had left—how much longer he'd be able to fight. His body still seemed in good enough shape, but he was itching to use it even more than usual, as if it might be gone soon. There wasn't urgency—yet. This, at least, was somewhat comforting. If it took another year for Goku to start worrying as he himself did, well—they might still be in good enough shape to—

"I don't wanna."

"To...what?" he blinked, wondering if Goku had heard him think.

"Get old."

Vegeta smirked a little.

"No offense, but it ain't no question whether I'd look any good with a scruffy face." He laughed, but touched his own chin thoughtfully. "It sounds kinda dumb, but...y'know...I was ready t' die a long time ago. I'm happy livin' now, and stuff, but I don't wanna die old."

Again Vegeta closed his eyes, wishing he could massage away the knot in his throat. "Reasonable, for once," he managed. Shifting position, he opened his eyes and looked at his reflection in the stream, expression disturbed by the moving water. Goku came closer, leaning over the small ledge to look in as well, and then dipping his head further down to dunk his face into the water. When he resurfaced, he held a fish in his mouth, and Vegeta chuckled. "You'll fall in one of these days."

"I guess," he laughed, holding the fish in his hands. "But, I dunno, I can't help it. It's just so easy to catch fish!" Appraising the one he grasped, he shrugged and tossed it back in.

Vegeta watched it swim upstream. The other men who fished here would probably disagree with what he'd said—but it was just another one of those abilities Goku had, maybe: catching fish.

"You ever gone swimming in here?"

"No."

"Wanna?"

"No."

"Well you wanna do something, that much I see, but if you don't tell me I dunno what it is."

Of course he wanted to do something—scratched at his hair again, wondered, cursed that he was so much older physically than the other Saiyajin, for all the time Goku had spent dead while he was alive and wasting away. "I'll bet you do know," he mused. Goku always seemed to know, and this would be no different.

He smirked a little. "Yeah. I think so."

...

"Today, huh?"

Vegeta was glad they had left the Earth so early—so quickly. He had had the ship there with them, after all; likely Bulma had not noticed the absence of that capsule until weeks or months later. It had taken so long to find the right place, wide and desolate and light-years away. The graying of his hair had slowed down—but every day he knew he was closer to the end, grew more desperate to jump in instead of walking peacefully downstream. This way, the water would be bloodied, and he would leave no footprint regrets on the bank for someone else to decipher. They would see the blood, and they would know.

"Dunno if I've ever been so far into the West corner," he noted offhandedly at Vegeta's continued silence. The prince nodded vaguely. "So, do Saiyajin do this?"

"Never knew one who got as old as we are."

Goku grinned a little. "Well, we're doing it. So I guess this is what Saiyajin do."

"Guess so." Vegeta smirked. "You look excited."

"I am!" he bounced on the balls of his feet. "This ain't a sparring session. It's gonna be the best fight ever!"

It was odd—to have someone so readily agree with him, and on such a matter as this.

"I've never wanted t' go all out so much," he balled his fists. "Neither of us got nothing t' want to hang around for. We don't gotta worry about somebody dying. Just fighting." Vegeta's silence persisted, but he inclined his head in agreement. "Y'know, they explode those firework things on Earth when the year is ending, in the middle of the night."

"Yes."

"They're pretty, but they don't hang around. They just blow up, real bright. I remember once, they were so loud we could hear 'em from our house, and they woke up me and Chi and Gohan, back when Gohan was a baby." He waited again, and then grinned. "Our fireworks are gonna be so big they wake 'em up again, all the way from here."

"That had better be a promise."

"Don't gotta ask twice," he seemed giddy.

"Good."

...

Bulma glanced up from her lemonade as a bright flash flickered across the quickly darkening sky. Hurriedly, she picked up her phone and dialed a number whose digits were well worn from the keypad. "You catch that one?" she asked.

"You're lucky I wasn't switching over the memory card just now. Got some good data on it," the voice answered, and from the sound of it he was rapidly moving through a series of keystrokes. "I've got the computer breaking it down right now."

"Thanks, Trunks," she smiled a little to herself. Of course it would happen the moment she took a break from the lab. Her family found her to be just like her father had been—always working a project, no matter how old she was.

"You think it's them?" he asked.

"Yeah." She smiled. "I do."