I guess the only case we can examine is The Doctor. Whenever The Doctor uses a transporter, what traveling: the lights or the mobile emitter?
There have been many cases which The Doctor has become solid so other solid objects can no longer pass through them. If the object we are seeing being beamed is the mobile emitter, then is it necessary for them to be on a separate pad? I imagine the person accompanying The Doctor could just hold the emitter instead.
Both. Though regular holograms would immediately dissipate on arrival, since they’re separated from the projectors maintaining the holomatter.
The Doctor needs to externally reconfigure himself through the computer control panel to change his tangibility, he can’t just do it on the fly.
Transporting him as if he was a human, rather than just the emitter probably helps them in that regard.
It’s also unclear whether transporting just emitter instead of the whole hologram might risk damaging his holomatrix, since you’d effectively be forcibly removing the emitter. He wasn’t designed around having a mobile emitter, or with the ability to be transported.
The Doctor has controlled his intangibility with a thought (command) multiple times. He mostly does his own matrix reconfiguring since like season 2 when he gained his autonomy.