3 led pot light in bathroom blink when turn fan on for a second but stay off
It sounds like a bit of counter EMF is being generated by the fan motor. Enough to cause a flash on the LED’s . This would not be seen with incandescent and maybe just a slight glow with LED’s.
I have seen induced current from a hot tub induce enough to light (dimly) 2 led flood lights when the pumps and heaters were running on separate circuits. Moving the conductors away from each other helped but to completely eliminate the glow I had to shield 1 cable in the wall where they ran in parallel for several feet. After that there was no light emitted.