Sounds like someone removed the best part of your truck (the 3B engine) and left you with the "evil centre tap" system, used to run 12 V headlights in a 24 V truck....
Depending on how the engine swap (...and more importantly, the wiring) was finished up, your headlight wiring may resemble a stock '83 FJ-40 (unlikely), a stock '83 BJ-42 (also unlikely -- I doubt the P.O. re-fitted the 2F with 24 V electrics), or some butchered/home-built combination of the two (hopefully, they had a little common sense, and the wiring will be somewhat logical).
You say it's an '83 FJ-40, but originally came with a diesel. That would make it a BJ-42 originally. It would have come stock with a 24 V electric system that uses some fancy/evil tricks to power 12 V headlight bulbs.
If the gasoline swap was well done, you should find (by physically tracing each wire from); the battery(s), through a fusable link (please say the PO used one), through the fuse box, through the headlight switch, which may directly power the headlights, or trigger a relay that powers the headlights.
Regardless of how the wiring was actually implemented, it should at least resemble the above description.
If the wiring was done poorly, you might find some, or all of the original 24 / 12 V system still intact. There have been a few posts regarding the 24 / 12 V headlight sorcery that may help you figure out what WAS there, and at least you won't go chasing down any OLD wiring that is now defunct.
https://forum.ih8mud.com/showthread.php?t=69908
https://forum.ih8mud.com/showthread.php?t=68379
As mentioned, comparing the wiring diagram of a stock FJ-40 to what you have should help in theory, but unless the person who did the work tried to copy a stock system, the BJ-42 wiring for the headlights is vastly different.
If you do find relays (Toyota calls them Dimmer switches) under the dash that are wired to the headlight, are they Toyota parts, or aftermarket? If they're Toyota parts can you read a part number on them? (Don't think you're in the clear if a Toyota Dimmer Switch is labeled 12 V --- the 24 V system has a dimmer that's also labeled 12 V).
Until we figure out how your headlights are wired, you should try the general suggestion mentioned by the other poster. Also, read through the two links above, and report back with what you find. You'll either answer some questions, or find even more, but at least we can go from there...
Cheers,
Steve
btw, If you find any defunct 24 V electrics under you dash, you should box them up, and send them to me for safe disposal
