I'm still learning about cars, so I'd appreciate constructive help.
Yes, I have searched the forums and Google.

TL;DR - The car will be running, and occasionally when the A/C is turned on, the car will stutter, all the lights on the dash will turn off, then it all comes back on, and the engine keeps running. Only happens when A/C is ON.

I can be driving at highway speeds and the car will stall and restart, all the lights shut off, and turn back on. It is as if someone cuts master power from the whole car for a split second, and turns it back on causing a stutter.

Also noticed while stopped that it happens when the compressor cycles on and off.

It doesn't happen all the time. Just randomly. I can go a week without an issue, then it starts again. I noticed it does it when it rains, so maybe it's wires getting wet, or something.

Where should I start looking? fuses? wiring?

 

Try unplugging the compressor at the plug on the compressor and see if it still does it. (don't let the plug get wet). The condenser fan will still run. If it still does it, then remove the AC fuse under the hood. That should rule out electromechanical and narrow down if it's the compressor or the fan (or wiring inbetween) causing the issue.