The cooling fan will cut on when the coolant temp sensor is
unplugged, ALWAYS. If it does not the problem is either the
wiring to the relay or the logic module may have an issue.
On the '86 GLHS I used to own I had a similar problem with
the cooling fan. Turned out to be the connector to the relay
had a loose terminal that wasn't making contact on the relay.
You can test the circuit with a DRB. Go to the sensor test mode
or the actuator test mode (Can't remember haven't recovered
from SDAC-13 yet) and test the relay. The logic module very
seldom will go bad in this area. The charging circuit normally
goes bad on L-bodies. But anything is possible. Keep us updated.