Air conditioning

You have a vacuum leak in the heater control system or under the hood. When you accelerate the throttle opens farther, that actually decreases the amount of vacuum and the actuators that hold the mode doors in position move and shut off the vents.

Common reasons for this are a bad vacuum check valve in the line to the vacuum reservoir or in the lines from it to the various items it holds vacuum for.

The reservoir is inside the passenger fender, you remove the inner fender liner to get to it.

The vent actuator (thing that pushes the air through the selected vent) is driven by vacuum pressure (air pressure) in this car. The vacuum lines are rubber. Rubber lines that are under the hood dry rot over time with the constant warming up and cooling down of the engine. They can either leak or just collapse under pressure. All you have to do is open the hood, find the leaking vacuum line, and replace it. If it is a collapsed line, a link to a how-to guide is below:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

You probably do not need a vacuum gauge, just to find the leaking/collapsing line (s) and replace them. They can bought very cheaply from your local auto parts store.

So all you have to do is find the leaking line and replace it.

Thank you for the help. I have a direction to go now.

If you can access a smoke machine or rig one up they can pinpoint leaks real fast.
Google paint can smokers for builds and online places that sell them. Be advised that you want to use pure unscented mineral oil in them, stuff with scents and additives stink and can cause issues with breathing.