Alternator, voltage regulator, and the connections between...good idea to have them checked.

Switch near fuse box, could be the Antenna Switch. You don't mention if you rocked it up AND down or just on and off, i.e. 3 positions (up/center/down) versus 2 positions (on/off). It also would not be unusual for your antenna to not be working properly .... if it hasn't already been replaced with a manual antenn which wouldn't be electrically operated.

FWIW

E

I checked all those connections and fixed the ground on the alternator. I started the car with a new battery, I disconnect the battery and the same thing happened. There must be a short somewhere... Where should I look.

Oh, and the switch only has two positions. Thanks.

I found some cables that were disconnected from the engine bay, oil pressure sensor wire, water temp sensor wire, and some others near the radio that I had no idea what they did, but I just put some electrical tape over them and voila! No more problem, I am still going to re-wire my Z just to be on the safe side. I'm going to remove that dang radio and put a new one in. There is a bunch of cables that belong to the radio and the equalizer that need to be gone, it looks like a web back there. Thank you all so much for your help.