I have been trying to tap louder and also more ergonomically, and It seems that coming down is just high speed (elbow or wrist?), but pulling off is really a slight pluck; does one pluck with forearm rotation or by means of finger motion?
I’m almost afraid that my finger will eventually be injured by smashing onto the string; just how violent should this process be? 
Umm not violent…
Tapping doesn’t require any more force than playing the trill, or any other hammer-on/pull-off technique. It’s exactly the same mechanic, just with a right hand component. Of course, gain and compression will allow you to play much lighter.
I use a finger motion for tapping. Basically straight up+down motion. I can’t imagine the elbow would be much use, and the forearm doesn’t rotate. The wrist only moves to adjust hand position on string changes, but I don’t move the hand at the wrist joint to tap.
Perhaps I have unrealistic expectations about how loud it should be!
That was going to be my question actually. Is there a reason you want it to be so loud? The traditional ‘shred’ EVH type of tapping is typically a pretty light operation. It’s just supposed to sound like an ordinary legato note. It would almost be like…using only legato but wanting my pinkie to be way louder than the other fingers. Not saying there’s anything wrong with that, if that’s what you’re going for 
That said, I’ve seen other styles that are more percussive (or even pianistic) where the right hand tapping is heavier. Michael Hedges and Chris Broderick come to mind.
I definitely use the wrist a bit when tapping but agree with @LuckyMojo that it’s mostly finger motion - the knuckle right where the finger meets the hand.
no elbow.
I do press pretty hard with the right hand - at least as hard as the left. I wonder if that might feel “violent” at first. because you’re not usually making this kind of contact with strings with your right hand.
Agree with everyone else, the tap shouldn’t be that forceful. If you do it Eddie V style, you grab the top of the neck with your thumb, thus locking out your wrist and arm, but giving your index finger full range to hammer away. I tap with my middle finger, so I plant the palm of my hand against top of the neck, or hover.
The pull off motion of the tap is a bit of a snapping the string down, not much, but technically that is what is happening.