@John49
The original motor listed for 9/77-7/80 40 series LHD 12V is # 85120-90308. I believe this was superceded with a later number.
This is a quick answer. More research and comparison of photos can show perhaps what the latest replacement would be.
Here's the long answer:
As with all electrical pieces, powering up incorrect wire connections can cause irreversible damage. Scrutinizing the correct wiring diagram for your year and model should tell you which wire does which function--both from the correct switch to the correct motor.
Patrick here is a great seller, understandably cautious about definitively saying what motor you specifically need. If I were selling new motors I would have a policy of no returns, since one misconnection can mean a burnout destruction. Since you state an FJ43, it likely is Central/South American origin, and very likely could have had adjustments made to its wire looms.
The only safe way to add a wiper motor to your vehicle is to KNOW exactly what wires you have and know where they go, along with the functions of your specific wiper switch. Otherwise it's a risky proposition to just slam a new motor in there believing it will work just 'cause the connectors plug into one another. Toyota made some variations in what all look to be the same motor. And yes, with all the other necessary components, each complete setup works correctly. The issue is having everything needed match up properly.
Bottom line: you can do this, but a simple yes/no answer on what motor to buy is impossible without knowing all the other necessary data. Do some reading here on Mud about the subtle differences and replacements, crawl under your dash with a flashlight and map out your wiper system wiring from start to finish, read the factory shop manual for how the switch works and the wiring diagram in back to verify which setup matches yours. And then, do some careful test checking before energizing anything.
I know this isn't the answer you wanted to hear, but you're not simply replacing part of a known operating unmolested wiper system--exchanging the exact same part you have, since yours is AWOL. Unless, of course you are willing to gamble on a simple plug-in solution and have the funds to possibly destroy a number of motors until you luck into finding one that will work in your application.
You are welcome to PM me once you dig into this and I can share some info with you that might be of benefit.
Good luck.