Hugh. Well another headlight issue... I won't blab too much guys.
-Combinnation switch, retract relay (blue box under steering column), fender retractor relay (black, bolted onto passenger side under hood)
-Fuses, fusible link
Might be a power issue thing here. Probably combination switch
Search Headlights and check out my old threads.

 

So it's not just the headlights, but all of the car's lights stay on?

I had a similar issue once, but it was because I reassembled the combination switch wrong when cleaning the wiper switch and hazard light contacts. My high beams stayed on when I got to work (after working on the car), so I had to disconnect the battery when I parked. After fixing the combination switch it was normal again. The lights had been stuck in the "flash" position, or passing headlamps. The rest of the lights did shut off with the switch, though.

Does your car have an aftermarket radio? There is a wire going to the radio for illumination, and if it gets fed power, the lights will stay on until power is cut. Hope that helps!

 

You have to have a volt meter to test these things with. Will not turn off is more likely a switch. You can check a switch with continuity and voltage on a volt meter. If you still getting voltage after the switch is off there's your problem. Then you can check continuity as well threw the switch. Dont Forget the TSRM listed on the site. Its the Toyota Service manual. There are electrical diagrams in there and troubleshooting to show you how all the wiring flows to and from switches and relays,

 

Ya Sowsley has those in his signature.
Good advice. Along with these guys, I have my money on your combination switch