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To clarify; I have not yet sprayed anything into the dial mechanism.
This used to be a light switch, but my son kept leaving it on. So I swapped it out for one of these dials about 2 years ago. Now it seems to be getting stuck around the 10-min mark and being left on all day.
I'd prefer not to replace this dial again; the house is old and the wiring in that receptacle was already pretty hard to work with. But I mean I'm not going to burn my house down in an effort to save myself 10 minutes and $10.
Is it safe to use a silicone based spray on it?
Silicone is non-conductive and will work fine. Another name for it is dielectric grease which is literally used to insulate electrical terminals from water and debris.
Your dial is probably sticking from the humidity in the bathroom while the shower is going. Keep the bathroom fan running when the shower is going to prevent humidity buildup.