I have exactly the same sound going on with my 2003 E, bennyG19. Your video confirmed that it's exactly the same noise. My girlfriend has been hearing it for months, but I admittedly suffer from hearing loss, so it wasn't until recently that I could hear it also. The fact that it's random, and RPM independent makes me crazy! :x I shall have to remove the glove box door and see what I need to rip apart to get at the damned thing. I intend to soak whatever it is in WD40 or silicone spray before I spring $45.00+ for a new blower motor. The blower works just fine - it's the random squeak that will eventually result in my putting a fist through the passenger side dashboard!
