Soft Cyclic Buzzing Noise
It took a bit of searching and collecting, but I needed to get my truck paperwork together finally.
The very similar noise that I had was the vacuum pump cycling on and off almost constantly. It seems the reservoir would not hold vacuum and the pump was overstressed. My dealer replaced the a "motor p/n 53032373AB" and the "Res p/n 55035614". The later description is difficult to read from the photocopy of the work order, but the diagnostic notes mention the "electric vacuum pump motor" and the "vacuum reservoir".
Apparently they had to go in through the top front of the truck to the upper part of the firewall. Their notes indicate they had to remove and replace the wiper blades, hood seal and cowl cover for access.
The primary diagnostic sounds pretty simple, "... pump motor cycling all the time; plugged vacuum lines; pump still runs. Tested res, won't hold vacuum. " The truck had 531 miles on it at the time.
I hope this is helpful.
Good Luck,
Brian