Chase down the matching neutral and remove it.
Otherwise it will drive you crazy, and be a loose end of wire unaccounted for. What's more, it could wind up still being in use by some other circuit which shouldn't be there. Part of the reason to fully explore an electrical system is to look for surprises.
Besides, since all wires must terminate in junction boxes, it will violate code and fail inspection.
I don't agree with my colleague that it's necessary to tear apart the ducting system, I feel unreachability is a defense. But to play that defense, you must positively identify both wires of that circuit, both where they enter and exit the ducting, and fully remove all of that.
There are two main ways of wiring a lighting circuit:
The wiring for the circuit goes to the switch. From there a live and a neutral are teed-off. The teed-off live is switched, and teed-off neutral unswitched, and then run from the switch to its relevant light fitting.
The wiring for the circuit goes to the light fitting. From there a live and a neutral are teed-off. The teed-off live for that fitting is then run to the switch and back, the teed-off neutral connects directly into the fitting. - This is the setup you have
It sounds like the new switch you've bought requires setup 1. There is absolutely no problem mixing these two setups. You could run a new cable from the fitting, taking the live and neutral together to the switch, and get rid of the existing cable to the switch.
Running the new cable may or may not be easy. In my house I can access the light fitting from above, as its in the loft. I can then find where the cable drops down into the wall to reach the switch, and feed a new cable through there (or tie it to the existing cable and pull through).
Best Answer
You circuit is wired without bringing the neutral wire to the switch box and so only the HOT wire comes to the switch and the switched wire goes back to the fan. For a traditional (i.e. dumb) switch, this works fine.
When you try to use a "smart" switch, and your electronic timer switch is such a switch, you have to supply power to the switch itself and that requires a neutral.
Two options: