Do you have a voltage tester? Fluke 88 or comparable? The direct hook-up is about the best bet. If it is good, check for connection at the ignition switch.

Will the car still push start? Assuming yes there but thought I'd check.

We had one here last week that had a faulty connection in the small tab that connects on top of the starter. I'd guess it was either that connector or a ground issue most likely IMHO.