I'm not sure what labelling you are talking about.
This thread is a bit confusing, since it was initially nothing to do with a fan, until the ('permanently on') fan appeared on page 2. However, what we have been told is that it is not a timer fan. and has only L& N terminals, but that it is (assumed to be, since that is what is seen at the rose) fed with 3-core cable, which appears to have cores connected to L and S/L at the rose.
Hence, regardless of whether a previous timer fan has been replaced at some by a non-timer one, the timer module has at some point been removed or the person who installed the wiring was making provision for a possible future timer fan, it remains the case that in order to come on and off with the light, the connection to the 'L' terminal of the fan has to be connected to 'the other' core from the one which causes it to be permanently on.
Is that not the case?
However, I'm a bit confused. Unless some recent 'fiddling with the wiring' has been undertaken, it would seem that the 'permanently on' fan will have been permanently on ever since the OP's friend moved into his new home - and that would seem a far more obvious/important thing for the OP to have initially mentioned and asked about than the feint glow of a switched-off led. I therefore wonder whether there might be something ('fiddling'?) we haven't been told?
Kind Regards, John