Rear heat/ac blower only works on low and medium speed

It will not correct fan speeds, you have other problems, perhaps heater core is partially blocked not allowing air to pass over fins. Look at blower motor resistors or high sped relay. good Luck.

Could be a number of thing's ! Testing the electrical circuit is the way to find out what's wrong . Using a wiring diagram and a DVOM - digital volt ohm meter . Videos on youtube showing how to test it ! Without testing i would only be guessing . Does it work in high speed ? In high speed it by-passes the resistor . If it doesn't work in any speed more then likely the blower motor is the problem !
Air Speed
The HVAC control assembly applies ground to the blower motor control circuit that corresponds to the selected blower speed. The resistors and the blower motor are in a series circuit. The following list represents the number of resistors in series with the blower motor per particular speed request:
• Low speed--3 resistors
• Medium 1 speed--2 resistors
• Medium 2 speed--1 resistor
When the operator requests High speed, the HVAC control assembly applies ground directly to the blower motor through the high blower motor control circuit. The resistor card has a fusible link which, if blown, will require that the card be replaced.

Blower Motor and Resistor Diagnostics by Wells

Buick LeSabre Heater - RepairPal

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Buick LeSabre Heater blows only cool air...even w/ defroster on. This is a ... Heater fandoesn't come on . ... The blower works but there is no heat coming out.

Blower Motor Problems ' Auto Repair Help - YouTube

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Buick Park Avenue Questions - NO HEAT!!! - CarGurus

depending on car some have a fan relay or its your switch itself

replace the switch

On any other vehicle it sounds like the blower fan switch.
The fan switch provides power or ground to the resistor and there would be a high speed blower relay to bypass the resistor.
But in your case the fan switch is part of the controller.
I don't have a diagram for a 92 but the 94 model shows relays for low medium and high speeds. Each relay gets power from a fuseable link. The high relay gets power thru the low relay if the low relay is not engaged.
If you have the model with 3 relays you may need to check them.

change the blower resister module,if this doesnt work replace the control head

replace the AC blower motor speed control resistor, it is burned out

U need to replace the blower motor speed control resistor.

if it doesnt work on all speed its the blower motor resistor that broken thanks pierre