The A/c light comes on, the compressor starts a spinnin and the idle kicks off, but the A/c light goes out and the compressor and idle keep doin they're thing. Any ideas? I thought the A/C light was controled by a signal that the compressor was engaged, so shouldn't it stay on?

 

The logicon (the a/c control unit) is known to go bad. You possibly have dirty contacts or cold solder joints in it. Search logicon and you will see what I am talking about:

Here is a link to get you started:

https://www.rx7club.com/showthread.php?p=9366500

 

throw the logicon on the ground and step on it.

another one of mazda's great marvels in electronics.