For starters, I'm not a tech, and I am not much of a car dude, but I've been working to change that since it's a lot cheaper to fix your vehicles then to take them to someone else.

Anyways, I've got a strange issue with the headlights my 1993 Toyota Pickup. It is the 22RE model. Here's the deal, my passenger side headlight went out ( or so I had thought), though when I switched the lights to hi-beams, the passenger side light turns on the and the driver's side headlight goes out. When the lights are switched to regular/low-beam, the driver's side headlight turns on.

From the bit of research I've done, it sounds like it could be a bad headlight relay. I checked the fuses and all of them are fine, though I was hesitant to check them at first, since the each of the lights do turn on, just not together. Am I correct in this guess or are there some other things I should check out to further diagnose the issue?

 

I believe 93 2Re headlight wiring is same a first-gen Runner 22RE wiring. Please look at schematic of your own truck.

Headlight relay will NOT cause your symptoms (see schematic below). Mad relay will affect both sides the same way.

This problem sounds like either:
1) One fuse busted or wiring from relay, through ONE fuse to that side headlight, OR
2) One busted filament.
Current leaking through remaining filament causes odd behavior.

I suggest you :
1) Double check your fuses . Resistance measurements not just visual.
2) Do resistance measurements on connector pins of bulbs. Pin 2 to Pin 3 should read low. Pin 3 to pin 1 should also read low. Both close to 1 ohm.
3) Take voltage readings at each pair of bulb connector. Look at schematic for color code.
High Beam: Pin 3 to pin 2 read 12V
Low Beam: Pin 3 to pin 1 read 12V

Then we'll go from there.

 

You have to watch those Mad relays!!

I just think you need two headlights.

one high beam is burnt out the other the low beam.

If what you stated is correct.

How long has this been like this??

 

Quick test: swap bulbs side to side, does the problem follow the bulbs?

 

Mine did the same thing, It was a corroded connection in the wiring harness on Passenger side, had to dig through the loom to find it.

 

Not a quick test. I believe it requires removal of the grill to remove/replace/swap bulbs, unless he had already converted housings.

YES, very good possibility.
Therefore, it is quicker to:
1) Take resistance and voltage checks in-circuit. and
2) Thoroughly inspect AND clean wiring, connectors and fuses.