you dont need an electrician to check a mechanical fan clutch
the only few characteristics of a good working fan are its behaviour at different temperature and events (starting up etc)
start up from cold
the fan should be loud and be blowing air pretty violently - this happens due to the silicone oil in the clutch settling out and dragging the fan upto speed. It will speed up with engine rpm
30 seconds from cold start
the fan should go quiet and slow down - engine rpm should not affect fan rpm.
engine hot (normal)
the fan should cycle in (get slightly loud or pretty loud at higher rpm) - it will be blowing lots of air.
engine rpm above 3500 (any temperature)
the fan should cut out (the clutch will go to off state and basically just freewheel) - the fan will suddenly go quiet.
If your fan doesnt behave as above - the silicone oil is low or the clutch is toasted.
You mention it has play in it, That is a very dangerous condition - if that fan breaks off the engine at even mid range rpm the damage will be quite expensive, namely the radiator, fan shroud, radiator pipes, bonnet etc. In the event of not noticing this - the engine's head gasket will blow out from overheating.
I would suggest replacing the fan clutch - buy an old one and refurb it.