Ignition experts needed

This is unbelievable! Brand bew pick up comes today. Put it in, set the gap properly and get ready to fire it up. Nothing. No lights, horn....nothing. Go under the hood and give the relay/regulator(don't know fer sure what it is), down by the battery a few taps, now it turns over and fires right up. Runs real nice for 15 minutes and just dies AGAIN. Same as before, watched the tach needle drop to nothing right as she dies. I noticed the dome light going dim, bright,dim and the volage guage was fluctuating also.
Now I'm mad. There's only 2 connections with this Accel ignition, one to the engine ground and one to a switched 12v ignition wire. So... I run the 12v wire right to the battery, completely eliminating all my car's original wiring. Fire it up and again, runs fine for 10 minutes and dies again. Crank away and no spark, wait 10 minutes and fires right up again only to die shortly.
The whole ignition system is brand new, and keep in mind this is why I replaced the ignition. I thought for sure it was the old system.

I'm at a loss for any clue. It HAS to be electrical, but what? I mean running straight to the battery should eliminate any wiring or relay/regulator right?

I saved for 12 years to buy this car and paid a lot. Now I feel like it'll NEVER run.
Somebody gotta be able to figure this out. I'm about out of ideas.

Mike