Having watched your video, if wonder if there used to be a pumped shower there. It may have been supplied by the lighting circuit and when removed the cable was left in the wall.mnow when you wet the wall the plasterboard is getting damp and causing a high resistance path to the live cable in the wall. If you go in the loft can you see any cables dropping down the wall above the shower location?
Sorry flyingsparks, almost missed your question.
I am 99% certain there wasn't a pump there, we've had the house for 14 years, the previous owners had it form new for about two and a half. There's no evidence anywhere in the loft (or anywhere else) of anything being installed, no orphaned screws or junction boxes in odd places etc.
Plus, all of the other showers are exactly the same type and install...