I will go through the options I suggested again.
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If you have a humidity sensor like in your fist post you said you had one then use a template sensor so when it is above above 60% (your request) then the by-pass turns ON or better option would be to use it to toggle to night lights with state condition and use a 10 min delay (your request for 10 min). That is if your not using night lights in the automation.
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If you get yourself a door contact sensor then use
Bee In The Hive Sensor template sensor. -
If you have a humidity sensor and something to control the fan then use my
Bathroom Humidity Exhaust Fan blueprint.
The best option would be 3 then the 2nd best would be 2 then 1 but they will all work.
Blacky 