Are you able to take out the glove box liner? I have a feeling the actuator in question is in that area. Wish I knew for sure...sorry.
Also have you checked all vacuum lines under the dash?
Try this...
With the engine off and key in the ignition in the acc on position......and fan on low speed....turn on the passenger side temp and move the temp up and down slowly. Listen for any movement behind the glove box.
Also do the same for the drivers side. Since you already know the drivers side works...listen how that side functions. Then compare the passenger side.
Report back when you can.

EDIT.......when listening on the passenger side...pay attention to any clicking sounds. If you here clicking, then that would be your typical broken actuator gear.

Although.....you have heat on the drivers side. Hmmmm.....yeah start with what was said already.

Ok I did some searching and found out that the two actuators are in the same general area. There is one on the bottom and one up top. I really dont know which one is which but I did find out the culprit. I had a vacuum hose that is spliced and was leaking. It was the purple one. Does anyone know what colors are what? So far so good. Ill be praying since we are supposed to get almost a foot of snow tonight and tomorrow and heat would be very nice.

The purple one or (violet) in the Bonneville'* is the main vacuum maker. Comes right out of the vacuum canister from underneath the front bumper..right side.

Sounds like you had enough vacuum to run the drivers side but not enough for the passenger side.

So did you splice the connection again?

I fixed the splice for now and this week if it ever gets warm I am going to replace it with a new one. Do you think if i tape the new one to the old one and pulled the old one through the fire that would work?

Nope sorry. I've tried. The darn vacuum line is taped to other things throughout the firewall. Unless you completely rip out the wire harness it'* attached to.

I would just make another good splice and be done with it.

good to know I glad you told me before I started ripping stuff out I probably shouldn't be ripping out with it. LOL

Are you able to take a photo of your dashboard for me?

I'm curious if your LSS has a cabin temp sensor.....if it does I would also check that as well. If its dirty it would send weird signals to the AC programmer.

On the Bonneville'* the sensor is behind the upper dash molding. It has slots in the molding allowing airflow to go through the sensor.

If your able to post up a photo I could determine where it is and then help you to get to it to clean it.

Yes I will post a photo of the dash and Ill post a photo of behind the glove box and try to describe what I have found out and what some of the stuff behind the glove box is.

Great Thanks!!