Blower fan will not shut off need to pull fuse.
Or you can lower the under - dash cover on passenger side and un plug the blower motor itself
SOURCE: heater blower not working in 1995 buick riviera
you're in luck... many aren't so lucky...1.5 hrs book time so it is under dash and no you do not have to remove dash to get to it .......be well
SOURCE: 1996 buick riviera blower motor will not shut off
The blower motor control module needs to be replaced, that will solve the problem. The module is underneath the hood on the firewall in the back. It has 2- 6mm screws. Unplug it, pull it out, put the other one back in. Plug it in. This is common for this model buick.
SOURCE: cruise control won't work, 10 amp. fuse in fuse box under hood ok
look at the other fuse box under the dash
SOURCE: 1996 Buick Riviera Cooling fan won't shut off. we
COOLING FAN IS CONTROLLED BY COOLANT TEMPERATURE SENSOR (CTS). REMOVE THE CONNECTOR FROM IT AND IT SHOULD STOP THE FAN.
OR JUST REMOVE BATTERYGROUND CABLE.
ITEMS TO CHECK OUT :
CTS,RELAY,CIRCUIT FOR SHORTS.
NOT LIKELY BUT IS A POSSIBILITY, THR ECU.
SOURCE: 96 buick century - lights/brake lights/dome
Check fusible links coming off of the starter, with the battery disconnected.
Pull on the various colored wires that have a barrel of foam on them about 1/2" to 2/3" long that indicated that the wire is a fusible link.
If a fusible link stretches, the inside of it is blown. Many circuits can be controlled by the fusible links.
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REPLACEMENT
Fuses protect all the major electrical systems in the car. In case of an
electrical overload, the fuse melts, breaking the circuit and stopping the flow
of electricity.
If a fuse blows, the cause should be investigated and corrected before the
installation of a new fuse. This, however, is easier to say than to do. Because
each fuse protects a limited number of components, your job is narrowed down
somewhat.
Fig. 1: Fuses come in different colors which indicate different
amperage ratings 
The amperage of each fuse and the circuit it protects are marked on the fuse
box, which is located under the left side (driver's side) of the instrument
panel and pulls down for easy access. To replace a fuse, simply pull it from the
panel. Insert a new (same amp rating) fuse in its place.
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