RNajarian's suggestion of simply trying the 3 various stock fan speeds built into the switch is a good place to start. These cars are are over 24 years old and the current demand on the stock fan speed switch is very high, hence switch contact issues.
Since the issue is the evaporator blower fan, the Thermostat is not the cause. When the fan speed switch is set to either 3 of its speeds power is sent from it to the Thermostat and not visa versa.
If trying the 3 different switch speeds does not resolve your issue, you can try disconnecting the evaporator blower motor's electrical plug, under the Smugglers Box lid in the trunk,
and power the evaporator blower motor using a separate circuit or power supply and let it run for 30 minutes and see if it stops running.
If it does stop running then you need a new evaporator blower motor. If it continues to run on a separate circuit then the issue could be
either the primary AC relay adjacent to the evaporator box, or the fan speed control pack located in the RH air inlet plenum under the RH foot board.
Here is the
AC Circuit.
If you get stuck feel to drop me a PM or email.