Isn't that pretty normal behavior? The alt light staying on until you rev the engine I mean. Giving it a good rev will tell the exciter wire on the alternator to start putting out juice. Maybe that is not normal on newer cars but it seems like that's the way old VWs are.

Does the static in the radio sound like a whine that increases and decreases with the RPMs? That is usually a bad ground somewhere that will cause feedback in the speakers.

Have you tested both the alternator and battery first?

On further exploration.  The antenna seems to stick when it cold so that may be some of the radio issues.  It has not had static when it is erect..  The alt wires all look ok but I have not done anything yet except wiggle them.  The light continues to stay on till it is reved

OK,
I had an Alternator do the same thing.
Eventually the rev'ing was not enough and I had to get a small ball-peen hammer and whack it..
Eventually that didn't work (read years here).
I then had to break down and buy a new alternator.
I was 16 and broke so do not judge me.
The guy at the parts counter just looked at the old alternator and frond with all the little dinks on it from the hammer hits...  LOL.
It was a honda so it deserved to be hit with a hammer once and a while.
KC