Only one 1987 Maxima Headlamp works at a time, dim/bright bulb alternates

Only one headlight works at a time, whether dim or brights. On dims, passenger bulb is on. On brights, driver bulb is on (after a few second delay, otherwise total failure to ignight). Rotating the bulbs (pass. for driver, driver for pass.) effect is same result. Is this a switch problem? A relay?

Well I doubt if it is the switch or even the relay, but I would look at the wiring from the relay to the lamps.

are you saying that when you switch bulbs from one side to the other, the bulb that is dim, is diom on both sides? same with hi beam bulb?

buy new headlight bulbs. it sounds to me that the high filament is gone on one side. and the low filament is gone on the other.