In general, an adult can get by just fine for fairly long periods with only limited rest before obtaining significant penalties. And yes, D20 really has no rules regarding sleep. As simple rule, yes, if you don't take 8 hours rest, you are fatigued. Forces the issue and isn't so blatantly unrealistic that you can't live with it.
If you really want to be realistic and gritty about this, the first symptom of sleep deprivation is not physical 'fatigue' per se, but mental fatigue. You might want to add a new condition that grants a very small penalty to intelligence and wisdom checks that represents a graduation between well rested and the more gross penalties of the 'fatigued' condition. The D20 'fatigued' condition is more appropriate to overexertion - for example, more than 8 hours of exercise per day, or prolonged periods of vigorous activity. It would in my opinion be more important to pay attention to what the party was doing with that extra time.
If my players decided to forgo some sleep but not all of it and work off of short days, I'd generally apply a very small penalty. My system as it stands makes it more important how comfortable your sleep is, than how much of it you get. That is, "Can you rest?", rather than "Do you get enough?" I've never worried to much about 'Is it enough' as no one has questioned attempting to rest taking a full 8 hours, so the following is straight out of my head without any testing.
8-6 hours rest per night: +1 cumulative penalty to endurance check needed to rest per hour under 8 hours. This penalty is reset whenever the character successfully rests for any length.
6-3 hours rest per night: +1 cumulative penalty to endurance check needed to rest per hour under 6 hours. This penalty is only reset if the character receives a successful rest of at least 8 hours.
3-0 hours rest per night: +2 penalty to endurance check needed to rest per hour under 3 hours rest. This penalty is only reset if the character receives a successful full 8 hour rest.
0 hours rest: You haven't attempted to rest at all. You therefore can't regain spells and are automatically fatigued.
Base endurance check to rest is DC 10, but a basic pallet (bedroll, straw, fur, etc.) and basic shelter (tent) bring that down to DC 6. Masterwork bedrolls and masterwork tents or hard shelter can bring it down to DC 3. There is also 'successfully pitched camp' bonus you can make with a DC 10 survival check to give everyone a +2 bonus on the check. Circumstance penalties for vermin (mosquitos, lice, fleas), moisture (sleeping the rain is not easy, and even tents can fail to keep you dry with enough rain), inclement temperatures (cold is likewise mitigated by blankets, furs or shelter), and wearing armor (armor check penalty) apply to the check.
So imagining a typical situation where a party made camp, pitched its tents, and everyone had a bedroll, it would be a DC 4 endurance check for each person to rest - trivial for typical healthy adventurers (about half my party can't fail that). If they decided to take a short rest of 6 hours per night, I'd just bump the DC up to 6. More telling would be what they wanted to do with that extra time. If they were trying to march 16 hours a day, that would be a much bigger deal and much more wearing on the party than simply getting 6 hours of sleep. But supposing the party wanted to go a long period on just 5 hours sleep (not sure when that would ever come up), there'd be like a +3 penalty the first night, +4 the second, +5 the third, etc. Eventually, it would get almost impossible to feel rested without taking a full 'rest day' to recuperate. Note that if the party was sleeping in a bed in an comfortable inn, it might take a fairly long time before that was true though.
(Well, for most of them. The PC 'paladin' of the god of travelers can basically ignore these problems, as he takes no penalty for forced marching and can deny something like the first 14 hours of needed sleep with no penalty at all. He can pretty much march at double time in armor for nearly 60 hours before even risking fatigue. He probably could walk 300 miles in two days, a superpower largely mitigated by the fact he'd be insane to split the party like that.)
Getting even an hour or two of sleep is actually a pretty big deal compared to getting none. None is hard. Napping even a short while has big benefits, as any soldier can tell you. Soldiers often go for days on 4 hours of sleep a night with only small penalties in alertness and vigor. Eventually, yes, this wears down even a healthy person but it takes a while and can be mostly reset by a single night of full sleep. Yes, eventually even this isn't enough to cure long periods of sleep deprivation but 'fatigue' is such a huge penalty in D20 that I think you'd not need to worry too much about metagaming sleep rules if you even had the threat of applying fatigue as a result of shortened rest.
