Xpelar silent bathroom fan with humidistat and run on timer

No, because you need a 3 core and earth to the fan via the switch. Permanent live, Switched live, & neutral. Edit.. I have just re read your question, when you said it doesn’t go on with the bathroom light I take it you mean it hasn’t got a run on timer? If it hasn’t then live neutral in appropriate terminals. What actually bothers me is you are messing with something that only has two connections to it and you are asking how to do it! Not really done is it? Instead of giving yourself a belt, or worse if unsure get a spark in to do it.