As a test try running the shower without the cover on, obviously make sure the shower head is pointed away from the shower and you and do not try and mix water and electricity (hang on that is what the shower does!).
If there is a leak then the water should spray out at that point when running.
Getting 3-5 Mohms on an IR test means that there would be a 76 microamp current flowing, I doubt this could power anything on an electric shower.
Generally switching the different elements is done with high power switches as microswitches could not manage the current.
So is this an electric shower or a thermostatic shower?
Check where the cables from the power light run to and see if there is anything wet, or damaged either at the power light or at the origin of the cables to the light.
The shower being on provides a very low current path for fault current and this may dry the area through current flow heating.
Electric showers are generally very simple things so a fault should be easy to spot, thermostatic showers are an entirely different beast and many electronic things can go wrong.