That's kind of what I'm thinking too.

OP if you can take a video that would help us quite a bit.

Also check and see if you have air bags or coil springs on the rear of the car, if someone has already done a coil conversion then their is no need to have the pump anymore

That was one of the noises, I stated above^

The clicking noise is one of the blend door motors more likely.
It comes on at key on and at key off?
Sound like the blend door,it will default in both conditions.
Normally the door will just open/close,you hear a clicking because the plastic gear inside the actuator is stripped more than likely.
Common issue.