AC vent doors

It sounds like the cables on the mode control box have come loose.
One of two things happens to the cable that opens and closes all the mixing and outlet vents on the car. They either pop out of a metal clip, The one that flips the vent doors open and shut are under the dash on either side of the heater core box behind the stereo to the A/C controls. With the doors pushed shut and the A/C on defrost, push the cable tightly in the clip. You may have to push on the clip some to make it snug.

The other situation is not as common but involves a broken plastic clip in the mode control. In this case, the mode controller needs replacement.

Sorry about that. I have an old Integra and sometimes the Z cars get those luxuries years earlier.
The way it is acting, meaning it is slowly closing, it sounds like a vacuum line a diaphragm actuator is failing.
In some systems there are electro-mechanical door actuators. The servos could be failing.
Either way the location of said components will be in the same relative areas as the cables and doors.
Pop off the shifter console and get a peak into what you are dealing with.
Getting a manual from your local parts store is adequate. The problem with them is that they cover so many model years and models. In your situation, the manual will be pretty model specific.
I researxhed and could not find anything for your car to help.

I will be doing some further research.
In fact I was going to re-join an enthusiast forum which is great fro this kind of hard to get information.

Let me know if you get the shifter cover off and can tell what type of controls you have.

I just found a forum called ProjectZ32. Com.
It looks pretty good, but I did not find anything off hand. Of course you need to join to searcha and I just don't have an e-mail that is free to add more stuff too.
I might try to get a new e-mail though as having access to these kinds of formus where you can ask people who have dealt with it all and know the car head to toe is invaluable.
So, I will keep looking. I swa a pic of your A/C controls and you still might get a look under the console and trace the vacuum/mechanical device at fault.