TASO test is saying that the T signal is only invalid on free kicks but that is incorrect. The T signal is an invalid signal on all kicks. 
At the moment, the "T" signal given while the ball is in flight from the kick is ONLY invalid on Free Kicks. I have heard rumors that the NCAA is considering making it
illegal invalid during scrimmage kicks, as well, but I have not seen anything to that effect, yet. If anybody has something official on that, please share.
Yes, any sort of signal - including a "T" - after the legally kicked ball is touched by a player or touches the ground is invalid. However, in 2024 (and before), a static "T" signal while the kick was in flight and untouched was 'nothing.' A Team B player could advance the ball after a catch/recovery following such a signal by any player. After some very 'visible' incidences of teams abusing this rule, the committee acted and has made the "T" signal invalid during Free Kicks (the rule change language is very specific). But, right now, Free Kicks only.