I pulled the yellow wire going from the ignition switch to the starter relay (at the relay) and it stopped the problem. I put a test light on the yellow wire terminal at the relay (with it disconnected) and it has power with the key in the run position. The test light only lights up in 'run' when the car was running. Weird??? Shouldn't this wire only have power with the key in the 'start' position? This is the one that energizes the relay when you start the car.

Another thing I noticed was the test light was dim with the car running but as I brought the RPMs up, it got brighter. Maybe this means as the RPMs come up, there is enough power to energize the relay causing the problem???

I traced this wire up to the firewall and it looks as though the previous owner tapped into it for the electronic ignition too.