Hi,
The connectors used by FO were really not intended for "external" use, I'm surprised they work as well as they (normally) do!
The magnetic switch may have stopped being detected, either because it is disconnected (or has failed) OR because there is leakage (a "short circuit") across the cables/connectors due to water ingress. The transmitter sources only a very small current (~30 uA) so quite a small leakage current can stop it working.
A "multimeter" would help to determine the type of fault, or even a "continuity tester" (a buzzer or lamp + battery) would test the cable and reed switch. Otherwise I'm afraid it's a matter of looking for corrosion, bent contacts or dampness.
Have you seen
this sticky thread which includes some photos of the inside of the anemometer (e.g. on page 2) ?
EDIT: If you don't mind upsetting the rain counter, you can plug the wind cable into the rain socket (and vice versa) on the transmitter. A functioning anemometer will produce
lots of "rain", or rocking the see-saw will produce a small, temporary "wind gust" (or about 30 tips for a 0.7 mph average over 1 minute).
Cheers, Alan.