OP, what is you skill level and do you have both an electrical multimeter and a scanner that shows live-data? This problem may even require a "dealer-type" scanner. First step would be to get a schematic of the circuit. Then, visually check all the pertinent wiring for damage from heat, vibration, rodents, etc.
I would like for you to give us the year of the land cruiser, and also trim level. Some trim levels have different wiring when it comes to power train. Such as is it a AWD or 4WD. I know it sounds the same but it is not and wiring may differ.
I will respond back once I get year and trim level, I will be happy to proceed, and yeah, as billr asked also, what is your skill level so we can adapt our help to you