It is probably proportional to the rpm difference between a gear and its next one (again, can't try myself). Usually the 1>2 gear change is the one with the largest rpm difference.
The problem is that the gear change fails
before you release the clutch. That is, you push the clutch in, select second and the game says you're still in neutral. Do this exact same thing with 3rd to 4th and there's no problem. It seems there is a minimum time limit required between engaging the clutch and selecting second gear. Sadly, it also seems to apply coming down as well, so decelerating into second gear (e.g. heel and toe) can be a nightmare, as can drifting (which is further compounded by wheel spin issues; the wheels must not be spinning when you try to engage another gear or it will fail in a similar manner.)
This is further hampered by the decision to force the player reselect the gear with the clutch in again, in order to recover from missed shifts. I.e., deselect gear, engage clutch, re-select gear, disengage clutch, continue. Ideally, you should just be able to dip the clutch and continue, because you've already taken your hand off the stick (there is no tactile feedback to tell you the gear wasn't found, so you can only tell by ear when the car revs freely instead of accelerating; in a real car, you'd feel that it hadn't gone in, and immediately retry with your hand still on the stick. A gear "grinding" sound or something would be a halfway point, but there's still no immediate reason to keep your hand on the gearstick.)
They really need to overhaul the driveline physics in general, though. You can stop on a hill (facing up it) in first gear, holding yourself with the brake (not the handbrake, obviously) with the clutch in; release the clutch and you'll stall. Now release the brake and enjoy the ride (it does that weird low-speed shimmy thing)!
Similarly, engaging first whilst already rolling backwards locks the driven wheels completely, whereas in reality, the momentum would probably turn the engine (how else would a jump-start even work?). Likewise for reverse when rolling forwards. Granted both of these things are likely to do some damage in the real world, probably mostly the gearbox and engine mounts, but that's not the point.
The clutch does not transmit enough torque when slipping, so starts are a nightmare of a balancing act; too much throttle and you over-rev (which is aesthetically annoying), too little and you'll definitely stall - the middle ground is very narrow (making this effectively a throttle axis issue, rather than clutch axis when the clutch is held still; of course, the excess slippage is more or less constant with clutch pedal travel before it transitions rapidly to "direct drive", causing the perceived "step" when you naturally try to feed in a bit more clutch, and a bit more, and too much...)
This also applies to gear changes themselves if there are large gaps in ratios or the engine is high in inertia; which is relevant to all in-game shifting methods and controllers (flat shifting would really show this up if it were allowed). The excess slippage / low torque transfer generally means gear changes take too long, and limit progress whenever the clutch is "slipping" - oddly, this could actually be an inertia issue, or at least be compounded by it.
Releasing the throttle when the wheels are spinning should result in them stopping almost immediately, but they gradually slow down instead (exacerbating the gearchange issue above). This smacks of dodgy tyre model, but I suspect incorrect drivetrain inertia is not helping either.
Hold the engine at a steady speed when stationary in neutral with the clutch in; releasing the clutch should cause the revs to drop momentarily as the gearbox catches up to the engine speed (constant mesh boxes only; but most are). Adding this modelling will give all sorts of other dynamic effects related to inertia, including "bunny-hopping", gear change "wobble" etc.
Over-revving the engine by changing down too soon does result in a clutch-slip effect at the rev-limiter, so that the engine will not spin any faster. It doesn't bounce, though. Because the clutch doesn't transmit enough torque, the effect of over-revving on the driven wheels is severely "nerfed"; this may also be why heel and toe rev-matching isn't that critical in GT5 (although 2.02 seemed to improve that slightly.) It's true that devices exist that can do this, but as far as I'm aware, they only really get used in motorcycles (and some four-wheeled motorsports, e.g. F1 - see "back-torque limiter" and "slipper clutch"). Further, cars with a frontward weight bias and rear-wheel drive will probably sooner skid the rear tyres before over-revving, but that would be catastrophic for your current heading.
This "magic rev-limiter" is not unique to GT5; most games, even many "proper sims", do it. This is no doubt partly because the sound samples would be hilarious / buggy at speeds above what they're "meant" to be played back at. Some games account / compensate for that by destroying the engine immediately when over-revved (boo). LFS allows over-revving, but it uses a "pulse-train" synthesis method for its engine sounds, so it doesn't sound weird at those elevated speeds.
Note that much of this affects most players, not just wheel users. 👍