I have the same exact problem,
for the past 6-8 months, I hear this noise coming from the back of the glove box, and it is not the cabin filter. It does sound like a pumping noise or as I would describe the noise as some sort of electromechanical relay switch turning on and off. Lately the sound has changed a bit and sounds more like a pump squicky noise. I have taken the glove box out and looked at the components in there but could not figure it out.
I ran the AC on and off but I didn't think it was unrelated to that. And just in the past 2 weeks, the sound is gone and my heater is not working, but the AC works.
Any suggestions?
Thanks