Yes that would handle the lights, the running issue I'd check for the ground at the head to firewall, at the fender and battery, then at your ignition coil.

I thought about the relay once before but I thought to myself if it was a bad relay then why does in turn on and off instead of just staying on all the time? I think your right about there being a bad ground somewhere, but where......i'm not sure. The coil ground and fender to battery ground are both in good shape and properly connected but I'm not too sure about the condition of the head to firewall ground so i'll check that first when I get some time.