Thanks for all the good tips. I currently have several of those LEDs with a sensor as well (they run on batteries). Went to a couple of shops after seeing the replies and realised that my idea is not feasible: anything on batteries lasts from 4 to 9 hours, and rewiring is not possible. Long story short, we put her on a waiting list for a nursing home yesterday. I realised I have no more tricks upon my sleeve to help her out. So for the remaining months, until there is a free spot, I decided to just stick with leaving the light in the toilet on 24/7.

Again really appreciated all the feedback, gave me some really good insight and helped making this decision (how weird that may sound from a total stranger, in the end whether they can go to the toilet without any guidance is one of the main factors if you can take care of someone or not).