[bonza]

I also have a 79 series land cruiser that uses the same system. a sentry key that has a chip and a completely separate fob with a battery to send a signal to open/close door locks

the chip in the key has a unique code that receives a a radio frequency signal from the sentry key immobiliser module (skim) that is adjacent to the ignition switch and has a round antenna wrapped around the key barrel. when the skim reads the key and verifies the code it in turn ok's the pcm to allow engine ignition. the whole system is called sentry key immobilizer system (skis)

the electrical power is in the skim, not the key. just like antennas do not need power to receive signals.

keys with batteries have the ability to do other things, like open doors, whereas my cruiser like the jeep has a key with just a chip, but a separate fob with battery for powering door locks

I think you find those you tube clips about replacing key fob batteries are those type of keys for remotely closing and opening door locks as well. nor powered door locks on a TJ

to the op, does the the skis warning light stay illuminated? a scan tool should detect any skis related dtc's. if not I'd be tracing earth faults

I'm an engineer, but not electrical and certainly no expert so am happy to stand corrected