Right mirror replace - 1991 Buick Century

see if this link helps you out.
How to fix right side mirror heater Google Search

I is likely the mirror has failed, but the switches can cause this as well, replace the mirror switch first. The mirror is big dollars, even higher if it is color matched to the vehicle paint scheme

they snap into place but should be ablt to get the spot mirror to replace

if memory is right there is a black cover in side the door that pulls off then the bolts are there to change the mirror

HOW DO YOU REPLACE OUTSIDE MIRROR ON 99 CHRYSLER

www.burcoinc.com
goto 'redi cuts
goto 'instalations', here it tells you how to replace all the different styles of mirrors. I think yours is a "snap fit / drop fit". You can buy a replacement mirror (like a burco) from your local glass shop or check with your dealership (but they may want to sell you the entire mirror head assembly)
*******make sure you get an automotive mirror (FMVSS 111 approved) Not house hold mirror that someone has cut.*******
hope this helps

There are two power wires to the DDM - drivers door module .Both are orange ,one is powered by a fuse DDM fuse 15amp . in the left I/P fuse block , plus LT DOORS 25amp circuit breaker .
Power Mirror System Components
The power mirror system consists of the following components:
• The driver door module--Class 2 module with integrated switches and requires programming when replaced
• The passenger door module--Class 2 module with integrated switches, requires programming when replaced and also contains the RFA receiver
• The power mirror direction switch--Integrated into DDM and is a 4-position momentary switch that provides a signal input to the DDM for up, down, left/extend and right/retract with a mirror switch activation
• The mirror select switch--Integrated into DDM and is a 3-position switch that allows the operator to select the left or right mirror and also a neutral/fold position
• The left outside power mirror--Contains both the vertical and horizontal mirror motors and is serviced as a complete mirror assembly
• The right outside power mirror--Contains both the vertical and horizontal mirror motors and is serviced as a complete mirror assembly
• The body control module--Class 2 module that requires programming when replaced, serves as the power mode master and is the main message handler
• The DDM 10A fuse--Located in the I/P fuse block and is hot at all times
• The PDM 10A fuse--Located in the I/P fuse block and is hot at all times
• The memory switch, if equipped with memory mirrors--Supplied power by the DDM and provides a voltage signal to the DDM upon a switch activation
• The horizontal and vertical position sensors, if equipped with memory mirrors--Supplied a 5-volt and low reference by the DDM/PDM and provide a variable voltage signal to the DDM/PDM that is proportional to mirror position
• The park neutral position switch, if equipped with memory mirrors--Provides transmission gear selection information to the PCM and is used for memory recall and mirror tilt in reverse functions
• The powertrain control module, if equipped with memory mirrors--Class 2 module that requires programming when replaced and provides Class 2 message indicating transmission gear selection
• The driver information center (DIC), if equipped with memory mirrors--Part of the instrument cluster which is a Class 2 module that requires programming when replaced and is used to personalize the memory recall and mirror tilt in reverse functions
• Fold motor in each of the outside mirrors, if equipped with power fold mirrors--Provides extend and retract movements of the mirror and is serviced as a complete mirror assembly
Each of the outside power mirrors contains 2 reversible motors to provide horizontal and vertical movement of the mirror glass. The vertical motor operates the up and down directions and the horizontal motor operates the left and right directions. If equipped with power folding mirrors, each outside power mirror will contain a reversible fold motor to operate the extend and retract functions. Each of the mirror motors are circuit breaker protected.

Do you know what DTC'S are ? Diagnostic trouble codes
DTC B1544, B1600, or B1605
DTC B1580, B1590, B1610, or B1620
• If DTC B1580 is set by itself, the left horizontal position sensor signal circuit maybe open, shorted to ground or battery
• If DTC B1590 is set by itself, the left vertical position sensor signal circuit maybe open, shorted to ground or battery
• If DTC B1610 is set by itself, the right horizontal position sensor signal circuit maybe open, shorted to ground or battery
• If DTC B1620 is set by itself, the right vertical position sensor signal circuit maybe open, shorted to ground or battery.
• If DTCs B1580 and B1590 are both set, the left 5 volt reference or low reference circuit(s) maybe open, shorted to ground or battery.
• If DTCs B1610 and B1620 are both set, the right 5 volt reference or low reference circuit(s) maybe open, shorted to ground or battery.
Need a factory scan tool to test !
Install a scan tool.
Turn ON the ignition, with the engine OFF.
With the scan tool, observe the mirror horizontal and vertical position parameters in the Driver Door Module (DDM) and Passenger Door Module (PDM) data lists.
Operate both the left and right mirrors through the full range of movements.
Does the scan tool indicate that the left and right mirror horizontal and vertical position parameters are within the specified range?
0.50-4.75 V.
Your best bet , take it to a GMC , Chevy , buick or cadillac dealer

The small triangle cover on the inside of the door pops off, just clips. There is a black circle plug just in front of it. These will give you access to the 3, 10mm nuts to remove the mirror.