Voltage problems, cutting out when hot

Something is haywire. You are talking about unplugging the switch and reading voltage. You are getting this on the bulkhead end of the harness and not the connector on the ignition switch end? That wire should be dead

But further, may not tell you anything to probe with various harness parts disconnected.

"Let's say" you have a poor contact in the ignition switch or in the switch connector in the "run" circuit, example.

If you read that voltage at the switch connector, everything connected normally, the CURRENT DRAW of the loads connected to it will cause a low reading and alert you.

But if you take the same reading with the loads/ connector unhooked, it may well read "normal."

If you have the switch disconnected........and are reading the connector half that leads to the bulkhead.......and if you showing voltage on either the yellow start wire or the blue run wire...........something is feeding back there someplace, possibly the fans??