I just got a '65 Mustang coupe. We turned off the key and pulled it out, the car was still running!!!

Soooo, we replaced the ignition. That was a frustrating process but it didn't solve the problem. Now we have been told we need a new "wiring harness". We are going to a swap meet this weekend. Do I need an "ignition wiring harness" or a "complete painless wiring harness"? My husband and I are totally ignorant but please have patience with us we are trying to learn.