Intermittent Ignition Issue [66 Valiant /6]

IF YOU shorted, and I mean FOR SURE shorted the large exposed contacts on the start relay, and the engine DID NOT crank on the starter, you have something else wrong, and you may be on the wrong track, IE the ignition switch may not be THE problem

Clean check the battery terminals. Turn on the headlights, are they bright? Short the starter terminals. Any spark? Any sound at all from the starter? Check the battery cables, battery post connections, and ground at the block from the main battery ground cable, and the cable to the starter

Wiggle the cables, check for loose, heat, sparks, etc.

Also suspect a defective or dead battery