This is a quickie step-by-step for replacing the A/C mode actuator motor, will be the same for all the '88-'94 with A/C and probably extremely similar (if not the same) for the '95-'98.
The factory service manual says you need to remove the entire dashboard to access this part. Not true! It's not easy, but considering it took me exactly an hour - I'd say it's far better than removing the dash. Takes somewhat small hands and no small amount of patience!
Tools used: 1/4" ratchet, 7mm socket, gasket scraper, 1/4" wrench, 7mm nut driver style bit. Picture of old motor shown for screw location reference. The one to the left of the yellow label is readily visible from under the dash. The one to the right is the tough one, positioned above the motor when in place, and impossible to see. One towards the harness connector actually just slips over a plastic locator dowel, no screw used.
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Remove the harness connector and the lower screw. The 1/4" ratchet and 7mm socket can be used.
For dealing with the upper screw, I pulled the glove box insert and crammed my flourescent work light as far back against the firewall as I could make it reach. While you're in there, pull the wiring harness for the actuator motor up out of the way.
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Here's a floor's-eye view of the motor; you can just barely see where the worklight shines down from above without being in your way to reach in, but helps light up the area where you'll be working.
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Here's where the fun comes in. Since almost nothing would reach up in there for the upper screw, I had to improvise. I put the nutdriver style socket onto the screw head by hand, then while laying on my back on the floor, positioned the gasket scraper with my right hand to press against the end of the socket to hold it in place. Then with my left hand, used the 1/4" wrench to turn the socket. A few turns and it'll be loose enough to turn the socket with two fingers. Then just gently wiggle the actuator off the flapper shaft to remove it.
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Before mounting the new actuator motor, connect the harness to it, turn the key on. The actuator motor will run and position itself. Turn the key off. I found this easy to do "up top" with the harness connected to it in the glove box area, then disconnected it to mount into place.
Here's a quick post-mortem on the old actuator. I opened it up expecting to find stripped gears or other damage, but there was no visible problem whatsoever. While observing its behavior compared to the new actuator, all I can guess is that there's a dead spot in the electric motor. It got out of place due to stopping early, and the A/C control system isn't designed "smart" enough to know where the actuator position is; it just sends it juice to run one way or the other and expects it to comply. Once I manually bumped it past its knocking position, it no longer knocked, but wouldn't complete the sweep needed to open/close the fresh air flap.
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p.s. the other actuators in the system (there are 3 total) aren't the same, You need the one for the recirculate flap.