Exhaust fans with a UL listing for installation over a tub or shower on a GFCI circuit can be installed over a tub or in a shower. This applies to most exhaust fans with light. Units that include any type of heating function to them are not able to be installed over a tub or shower. Here is a link that might be useful: Chandeliers Brisbane

I have experienced this issue (fan randomly coming on in the night) and believe I have found both the cause and the solution and would like to share it with you. Firstly this is to do with an inline fan system where the fan draws air out of a shower light assembly and then pushes it out through an external vent. The problem is moisture getting into fan timer electronics which causes the circuit to switch the fan on, sometimes with irregular pulsating speed. The solution will be to remove the timer circuit board and dry it out. However, you will need to make sure it doesn't happen all over again. There are two things I did in an attempt to make sure the problem didn't reoccur: 1. The wires from the fan (the fan is in the moist air flowing along the pipe) connect to the timer circuit through a channel in the fan housing. Air can also travel along the wire channel bringing moist air with it where it condenses. Use a sealant to block the channel before replacing the timer circuit board. 2. The air will be forced down the wire channel if the outside vent becomes blocked - it will try every route to escape. Keep the outside vent clear. In my case it was blocked with lint and fluff. Hope this helps

Thank you all for the responses. It was the switch. This is what I did - 1. At the breaker- cut off the power to the fan. 2. Unplugged the fan plug at the top and then tested to see if I am getting any power at that outlet and there was none. So this concluded the decision to go for a new switch. 3. Replaced switch and now it works. Jim - Prior to this I found a dead bug and the bottom right black wire was unscrewed. The switch was broken at the back too. Regardless even after tightening the screws it never worked and then I did the above 3 steps. Thanks for your help, this saved me $$ to call an electrician.

"Does the mirror get hit with heat from a secondary heat source like a towel warmer?" No. "Is the mirror on an outside wall that gets heated up by the sun?" No. "Does sunlight from a skylight or sunny window hit it?" No. "Depends on how close to the shower they are, too, along with room temp, water temp, existing humidity." Shower is "small room, walls of glass, no ceiling," two steps from sink below mirror. Room temp is in 70s year-round, probably low humidity because of heat pump running a lot. "New fans are not very expensive and many are very quiet." In fact, I replaced the fan a few years ago. Wasn't quieter. My notes aren't complete. I find Broan 688K, but not sure if that was the original or the replacement. Replacement fan was also Broan and same size and connections as original. Maybe that's the best thing to do, is just find a quiet fan. "Just because they aren't fogging it doesn't mean that steam isn't affecting other parts of the room." But when I looked before, I couldn't find both quiet and simple installation. Maybe it was the size of the exhaust vent, I forget. Thanks for feedback. Appreciate it.