allison transmission cummins 300 neutral safety switch

Sounds like you don't have adequate voltage to the idiot lights and related equipment. Could be a ground issue. I would connect a voltmeter to a negative frame ground and check both the ground side of the lights and positive side.

ie Thinking that you have a partial open and with the additions load of the starter you lose the basic ignition components.

In fact I'd start at the ignition switch itself as it could be bad.

It might help to know just what you did/bypassed to get it started.