My go-to answer for anything like this is usually ground issues somewhere. I have not seen this exact senario, but if the grounds are good on the driving side and not on the passenger side, the current could be leaking back across. I'd try using some test lead wires with crocodile clips on the ends to to ensure a solid groud directly to the lamp housing and to a known good ground point (like the alternator mounting bolts or the radiator surround frame bolts) - clean the test point to good shiny metal on both ends.
In my B I took the extra step of adding actual ground wires to every lamp housing (except the headlights because they have a ground wire already) and bringing them back to solid bolt points with ring terminals. Solved every mysterious "why is that happening" electrical issue completely. If that isn't it, then someone (or something) did something in the wiring harness to cross those circuits up - look for rodent-chewed wires, evidence of poorly done work or hot/melted insulation.