Electrical – Bathroom light switch inoperative, but fan swith okay

Your ohmmeter testing has established that the switch enclosure is NOT grounded. (or you were hitting it on a painted or rusted spot). That's not a surprise given the vintage of the home. Stop measuring voltages to it... or air. It's futile.

Most likely your house originally had gas lights - that's something to think about if you have a chandelier or ceiling fan, because they often hung those from the gas line. The active, never-disconnected gas line. Isn't old San Francisco housing stock fun?

And you know those 2 wires that were never connected to anything? They're not needed obviously, so please identify them and exclude them from the following test. God only knows where they go to, and energizing power onto them could be a mistake.

If feasible, put an AFCI (Arc Fault) breaker in there. Those prevent house fires. A GFCI (Ground Fault) breaker prevents electrocutions by making sure all current going down a "hot" comes back on the corresponding neutral. Distinguishing the difference is diagnostically useful here.

Time to make a test instrument. Buy a cheapie extension cord. Grab it by the prongs, cut the cord, and throw the prongy part away (or plan your cut and use it for another project.) Strip the cut end of the cord back to expose hot and neutral.

Plug a desk lamp with an Edison base into the socket on the cord. CFLs and LEDs won't work for this - get matched incandescent bulbs. Put one in every lamp under test (remove others), plus one in the desk lamp. Get spares.

Shut the breakers off, wire-nut the leads to any two wires, have a helper turn the breaker on and see what happens. Do the same matrix you did before (leaving out the two mystery wires for now).

• If the test lamp and a fixture both light dimly, you have found a "line" and a "load". This is guaranteed to happen at least twice.
• If they are of unequal brightness, different wattage bulbs, no big.
• If the test lamp lights full brightness, you have found a "line" and a "neutral" or "ground".
• If the lamp lights very brightly, once, you have found two opposing "line" legs of 120V (240V between them). That is special, possibly a MWBC.
• If an overcurrent trips, you did something wrong, or bad wire.
• If a ground fault trips, it means you have found a "line" and a "ground". Or (not likely) a "line" and the neutral from another circuit. Or bad wire.
• If an arc-fault trips, it means the wiring just tried to set your house on fire. There's a remote chance it succeeded - inside-wall fires can take hours to develop - so stay around for a few hours.

That's why I'd start with an arc-fault breaker, especially if you're messing with those two mystery wires. A dual-mode breaker is OK if it can tell you definitely that it tripped for arc-fault and not something else.

Then get back to us and tell us what you find.

Please excuse my MS Paint representation, but it should help.

From what I understand, the grounding wires may not be necessary, but if the fixtures have ground wires or grounding terminals, it can only help to connect them. This question explains grounding in some more detail.

One exception is that if the vent is directly over a shower, it might need to be GFCI protected (see this question). This could be done in a variety of ways. You could install a GFCI breaker and run the vent on a dedicated circuit, but that would be annoying if it tripped since you could only reset it at the breaker. You may be able to install a dedicated GFCI outlet in the bathroom and connect the vent and switch to the protected side of that outlet. You can also find combination GFCI outlet/switches that would combine the GFCI outlet and the switch into one unit.