Coolant level sensor 101--

Disclaimer--I'm not getting this from any manual, so take with a grain
of salt.  Information based on archives and foggy memory.

Sensor uses coolant as a conductor.  As long as level is sufficiently
high enough, a complete circuit is formed.  Air is a very poor conductor
(duh).  Thus, too low a level of coolant breaks the circuit and SHOULD
make the light come one.  Likewise, disconnecting the sensor SHOULD make
the light come on since the circuit will no longer be complete. 
Incidentally, a light coming on while the coolant IS high enough could
indicate a) faulty wiring, or b) too low a concentration of coolant. 
This is because pure water, despite popular opinion, is also a very poor
conductor of electricity.

In all likelihood, your sensor is fine.  For a warm fuzzy, you should be
able to use a multimeter on the two pins of the sensor (while in
coolant) and read a relatively low amount of ohms (most likely not zero,
unless your coolant is a VERY good conductor, but close).

Since the light requires a completed circuit, your 'probable cause' is a
short in the wiring, i.e. somewhere along the lines the wires to the
sensor have been broken and are touching each other.  It could also be
caused by one being shorted to ground, but I'm not sure without a manual
to look at.  This can't definitively be checked at the sensor end
because the wires may have been shorted on only one side of the break.

Look at the path they take through the engine compartment.  They may be
laying on something that gets real hot (like anything in the engine
compartment!) that melted them internally somehow.

I'd really suspect wiring if I were you.  But again, note my disclaimer!

In regard to radiator fan, mine kicks on about 2/3rds of the way up, a
little past the light but not too far.  It usually only kicks on when
I've got the AC going, or am sitting in stop and go traffic.  For normal
driving, it stays the right temp so it's not needed.  It doesn't have to
stay on for long either as it seems to cool off back to normal pretty
quick.

Tonya
87 Vanagon GL
74 S. Beetle