As Mr. Tim says, the blinky red light mostly blinks because the level in 
the coolant tank on the left is low (or the contacts are otherwise out of
the fluid).  It sounds to me like you most likely have a blown head gasket
or a crack, and combustion gases are entering the coolant.  This raises
the pressure in the tank until it is relieved by the valve in the blue
cap.  The combination of gases in the coolant prevents the pump from moving
it about, and you end up overheating.  The blinky red light *is* supposed to
come on if you overheat, as well as if you're low on fluid, but since it
comes on first, it is likely that the well where the sensor sits is full of
exhaust gas.  If the crack or leak is really small, only small amounts of 
coolant will be lost, and then only at idle (when the vacuum is high). 
Blowing gases into the coolant occurs only when the combustion pressures are
high -- freeway driving under load, e.g.  When under moderate load, the
air/coolant mix will pump ok, and the multiple-vent-tank system on the VW
will separate most of the gases out of the coolant.

I don't know if there is a cure other than a teardown, but I'd suggest you
try a different mechanic for an opinion (other than mine as well -- I'm
an amatuer).

Another place to check, BTW, is the waterpump.  If the seal is going, it
is possible to get air into the system there.  They usually either leak,
or give up in a more spectacular manner, though.  I still bet on a 
combustion chamber leak.

malcolm