Those headlight connectors and crimped wires like to corrode and lose continuity. A poor connection causes additional heat which in turn causes the connection to arc and generate more heat - a vicious circle until the current flow is completely lost.

Check the wiring and the female spade connectors. The weak link may be hidden inside the plastic insulator.

I cleaned and put dielectric grease in the socket, which worked for a while. I ended up replacing the socket. Generic socket for high temp settings (like when the lights are on all the time) available online for a few dollars.

Bulb out relay is quite simplistic. If voltage/amps is low on one side, then that bulb must be out. You might consider cleaning the bulb socket and using dielectric grease, as long as the bulb is good.

Most people replace both sides to keep the current draw the same.
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Keeping it running is better than buying new