Hemi swap 6.1L Turnover, Pause Start Issue

Sounds like a blown fuse that supplies power to those circuits. Locate the blown fuse/ replace it/ if it pops again, unplug the o2 sensors/ replace the fuse again, if it doesn't pop, plug in 1 sensor at a time until the fuse pops, I have found the heater in a o2 sensor can short to ground just because. Or you may need to unplug the transmission connector or any item on that fused circuit. Do you have a schematic?

How could it be a blown fuse? If the fuse blows, there would be no power at all. His is losing connection and then regaining it. Just asking to understand.

I would pull the starter and bench test it's operation (see if you can duplicate). Maybe a faulty ignition switch?