My buddys 89' s13 was having the same problem, both headlights would pop up, but the passenger side wouldnt illuminate. It would however, light up if he turned his brights on, kinda weird. Well, I did some searching and found this great write-up here on NICO on how to fix your switch, and after what you've stated, it seems the culprit could very well be burned contacts inside your HL switch on the column (nothing serious, just from years of everyday use). He followed the write-up exactly and it worked for him, check it out, it's pretty simple and wouldnt hurt to try. Good luck!
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