*** UPDATE *** I've moved on to the interior of the car and am preparing for the install of my ICE system but before that I wanted to fix the climate control unit. I am one of the many Supra owners where the air flow direction buttons do not stay selected when they are pressed. After several attempts, I seem to have the problem fixed. To repair the problem you have to do the following:
1 - remove the console trim (3 screws)
2 - remove the climate control unit, it has 3 screws and 2 wire connectors on the right rear side, pull the unit out and have it hang down to gain access to these connectors.
3 - pop off the button faces of all the buttons with a very small thin flat blade, they seem to pop best if you pry them up from the sides.
4 - with 2 or more larger flat blades, pop the black front section out of the case by pressing down the tabs locates on the top and bottom of the case. Start at one end and push down the tabs on the top and borrom and use a stuby flat blade to pry the face out a bit (there is a square slot to put the screw driver in on the side), repeat on the other side then back until the front pops free. Careful not to pull it off as it is attached with 2 bunches of small wires.
5 - with a small flat blate, pry the connectors off the electric board inside the grey case by slowly working the blade between the connector and the socket from one side, the middle then the other until the connector pops off. There are actually 3 connectors, one side has a small and a medium one side by side.
6 - Remove the 6 or 7 philip screws on the green circuit board from the front part of the unit.
7 - With a small flat blade, pop off the little hook clips that hold the white sliding button from the structure under it. As you pop more of these off the circuit board will come loose. The clips are hooked to the inside sides of the sliding button except for the buttons that raise and lower the temp, these are on the top and bottom on the inside of the sliding button. There is no force her, just patience and seperating the sliding button from the structure under it. Once all the buttons are free, the circuit board will come free. The issue lies with a brass flat metal piece that is under the grey metal rail that holds the switches. You can see the tip of this plate right next to the button. This brass plate slides into a small tooth notch on the switch and keeps the switch depressed. The problem is that the brass plate corrodes and no longer slides easily under the grey metal structure. The spring force on this brass metal is very low so even the little corrosion will make it bind. I first tried electronic contact cleaner and air, this fixed things up for about 2 to 6 hours before the button problem returned. The electronic contact cleaner would become tacky as it dries up, similar to white grease so the brass plate woud stop to slide easily. On the last try I decided to use some oil (motor or machine should work fine) and lubricated the underside of the grey metal structure at each button; pressed each button to spread the oil around and then stood the unit up on its side to let the excess oil run out the end. After that, the brass plate moved freely and the buttons stayed selected. I guess the only issue might be for those of you that use your car in the cold winter where the oil will thicken and once again bind the brass plate. To put things back together, pop off the little castle looking parts that are on the switches (squeeze them from one of their sides and they unclip) and put them back into the black front face (sliding switch part). Be careful of the orintation of the AUTO button, the clip should align with the black post and not the white. When you put the electric circuit board back on, they will pop onto the posts, press the front part of the switch to make sure they pop all the way on once you screw the board back on. It took me about 15 minutes to dismantle the unit and about the same to put it back together.
If you have extra $$$ you can always buy a new unit (dig deep into your pockets as they are not cheap) or bid for one on ebay as they come up once in a while but still, they don't go cheap as they are in demand... Hey, with a little patience and time, you should be able to fix yours.