Cadillac has had their share of problems with the "power module" which
is a transistorized speed control device which takes the place of a
blower resistor.  I can't keep SeVilles and DeVilles straight, but one
or both of those models and their GM counterparts use a blower motor
which has an integrated power module.

Look under the hood on the passenger side firewall for the blower
motor.  If it has three wires going to it then you have this design
which is a high failure item.  Aside from the typical GM failures in
power modules, the motor is positioned near engine heat and can cause
quick death.  Even though your description sounds like the power module
is intermittantly opening, this failure can be caused by the motor
drawing too much current.  At any rate, the blower is an assembly so
test it and replace it if necessary.

While the blower is currently inop, check that one wire has 12v, one
wire is a solid ground (<.2v), and the third wire is aproximately 3-6
volts or so.

Test by backprobing the connector with it attached to the motor and set
the controls to operate the fan at a medium speed.

You say that the blower is accessible from the glove box.  If this is
true, then the bodystyle has changed on or around 2001 and it is a
different system.  Same test rules apply, but the power module may a
seperate unit mounted in the blower housing with self tapping screws.

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