Sorry, it's a 2001 SR5 2WD (I know, but I'm not going off-roading)
[MENTION=129567]Makitso[/MENTION] - It's not a Limited, so the climate control isn't digital, but it is electronic. And the sounds definitely mimics a lot of those noises. Could be the problem, but it's difficult to diagnose since pushing the button on and off doesn't necessarily cause the sound. It kind of just does it on it's own.
[MENTION=326755]rightyouareken[/MENTION] - Thank you. It is a 2001, so I pumped the brake a few times and heard the brake booster pump you're referring to. Very distinctive sound, but not my issue.
[MENTION=389448]Myjar89[/MENTION] - I think it might be the problem, but did your recirc work? Because mine seems to. I have a different airflow when I press it. And it doesn't seem to affect the sounds immediately. I can absolutely imagine a recirc door getting stuck when I hear the sound, but I also feel like I would be able to recreate it on command when pushing the button. Thoughts? Also, I live fairly close to a junkyard, so I can probably pull another door if it's the problem. The real question is how do you get to it?