Starter battery cables. I had one cracked at the clamp, barely visible, worked until you move it OR until you try to start the engine.
Dirty/oxidized battery terminal is possible, though after switching batteries back and forth it should've cleaned itself and it is NOT likely to have two batteries with equally bad terminals. Still possible. Wipe it with denaturated alcohol or whatever you have on hand, or clean it with sand-paper.
Clean and sand those lugs on starter cable too.
Both batteries dying at the same time? Maybe... Who knows...
