Do wingtip vortices really only form when airplane wheels are separated from the ground? My GA theory textbook (which covers fixed wing up to and including EASA PPL) has some suggestions on taking off and landing light aircraft soon after large aircraft (besides avoiding it, if possible), intended to reduce the risk from wingtip vortices. These suggestions are to,


when taking off


...after a heavy aircraft taking off, to lift off at a point on the runway before the heavier aircraft lifted off
...after a heavy aircraft landing, to lift off at a point on the runway later than where the heavier aircraft's nose wheel touched the runway

when landing


...after a heavy aircraft taking off, to land as early as possible on the runway
...after a heavy aircraft landing, to land ahead of the point on the runway where the large aircraft touched down



When I asked about the why of these suggestions, the answer was that wingtip vortices form because the wings are generating lift, and when the aircraft's wheels are on the ground, the wings don't generate (or aren't generating) lift so no wingtip vortices form.

While that might be true in a "rule of thumb" sense, and a good generalization of these rules to serve as a memory aid, I want a bit more than that. The way I understand it,


Any airfoil will generate some amount of lift as long as there is ambient air movement around it; "lift" (as opposed to net positive vertical lift, which isn't being generated when landing anyway because the aircraft is descending) isn't something that suddenly starts being generated when one or more of the aircraft's wheels are separated from the ground
An aircraft can move at significant speed relative to the surrounding air even when all of its wheels are on the ground, causing likewise significant speed of movement of the wings through the ambient air


It appears to me that wingtip vortices should form at any time the aircraft (or rather its wings) is moving relative to the surrounding air; whether that's because the aircraft is standing still and there's a wind, or because there's no ambient air movement and the aircraft is moving, or a combination of the two. It also appears to me that the strength of the vortices should be in some way proportional to the amount of lift being generated.

Consquently, it seems to me that wingtip vortices should form at every point during the takeoff or landing roll (as well as taxiing and other movement on the ground) at which the aircraft is moving relative to the surrounding air, and increase in strength with (but not necessarily linearly with) the indicated airspeed of the aircraft.

It seems weird that the air flowing near the wingtips would somehow "know" anything about the position of the aircraft's wheels with respect to the ground, let alone that of any specific wheel (such as the nose wheel).

All that just as the lead-in to my question: am I missing something, or is this a case of the textbook (and teacher) presenting the simple case so as to not overwhelm students?
You are absolutely right. The vortices form whenever the wings produce lift. Even if the lift is not enough to let the aircraft fly.

Of course it is necessary to have a flow across the wing, and with very low speeds (like taxiing) the vortex is likely to be very small.

But,
it seems your textbook is trying to establish a save way to avoid the vortices of previous aircrafts. And since the strength of the vortex is related to the lift which is related to the air-speed and angle-of-attack this rule of thumb is quite practical. Especially since landing is a highly transient process which is very likely to result in a significant reduction of vortex strength.