@skydriller You will, no doubt, have been given a squawk when on the ground. For most GA this will be primarily for use once in the air but suitably equipped ATC units can certainly use your Mode S ground mode to see you on their ground movement radar. The important bit here, as I understand it, is that ground mode doesn't transmit altitude and, therefore, your extended squitter will not be transmitting ADSB 'cos it doesn't have the full suite of info to do so. Because of this ADSB receivers don't get scared and give us nuisance warnings.
@johnm I think
FR24 is using an MLAT feed to provide ground traffic (through Mode S ground mode)........or maybe it doesn't, having just read Graham's post above
I suppose another option would be for SE2 and similar, to not provide warnings below, say, 100'. Similar, in a way, to the way TCAS changes its modes from RA/TA to RA to no descent RA as you descend.
My 'air switch' works through a combination of speed and engine RPM from the EFIS to let the transponder (and ADSB) start doing its job. I know it doesn't chuck out ADSB on the ground because I've had to disable the air switch in the past in order to be received on another person's ADSB In device when he was testing it.