I have worked out the wiring (which is how I first proved that the
humidistat was on most of the time) but I would like to fit a small LED
which only lights when current is passing through the switch.


Did you get your answer yet, David W.E.?

I read most of the thread but couldn't see any simple answer...

As far as I am concerned, you need to look at the *current* flowing
through the switch (or the humidistat), as I guess they are connected
in parallel...

I saw a circuit using a LED and a few diodes, which in effect will
monitor the current. It was used as an indicator for a normal (no
neutral) 240V light switch.

Quote: (for 'Lamp' read 'Motor')

fixed width font
LED
----RES180R---||----
| |
SWITCHED-FEED----||--||--||--||------LAMP
| |
---------||---------

--||-- = DIODE

A bit heavy on component count but lights evenly independent of lamp
load, choose diodes to match full lamp current. LED is low current
(5mA).

All parts are live, including the LED. For safety don't poke the led
thro the panel, use a plastic holder.

Extra components would be required to meet BS/VDE safety.

Unquote... (from uk.diy - "Power an LED from a light switch?")