jbowser has the probable answer - bad ground. The headlight harnesses for that year are each grounded via a small dia. black wire that is fastened to the inner fender. For the left side it's behind the battery. Jumper the ring terminal for that ground wire to the battery negative post and if the high beams light up there's the problem. Remove and clean that ground terminal and the fender area it mates with. Do the other side too - it's behind the windscreen washer fluid tank, and it can't be far behind on the trouble trail.

So why do the low beams work? Grounds are funny - they can be just good enough to allow a certain load (current) to pass OK, but when you double it (eg: high beams, here) the ground gets hot and goes open circuit.
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Bob (81-244GL B21F, 83-244DL B23F)