Got a Gremlin

Sounds like an electrical problem for sure. A new coil doesn't always mean a good coil. Did you replace the ignition resistor?
http://www.mopartsracing.com/parts/electronic/restrore.gif

Where is that thing located?

electronic ignition??? if so id check the back of the ignition box for melted epoxy. My ramcharger would do the same but its fuel injected and it was the magnetic pickup in the distributor

No, not electronic ignition. But thanks!

Try changing the reluctor in the distributor (little square black cube). they crap out at any time and start working usually after they've cooled down.

Never heard of this. Is there a way to test it?

Was hoping to see an AMC Gremlin X with the Levi's interior. Good luck with your ingition issue.

And you see...I'm from the eighties, so when I think "gremlin", I think of a little green monster that multiplies in water! Sorry to disappoint!