I have a relay like that makes the same noise on my Coach (but I don't have that rear circuit board on my '05).
On my Coach, in the front Run Bay, there is a relay for the bay door locks, and that relay buzzes like that every time I turn off the Battery disconnect and turn it back it on.
I have to enter the unlock security code on the keypad at the entry door to stop the buzzing. It seems to be related to the (Essex 1704) "Keyless Entry" system. Once I enter my "unlock code" the buzzing stops and all works as it should. I know it shouldn't do that (buzz) - but I haven't had time to look into the cause. With the front Run Bay door closed I can barely hear it. I think it was buzzing for over a week (after I turned Coach power back on) before I noticed it, and figured out what it was.
I don't know if that board in your video has anything to do with Keyless Entry or not, just mentioning my issue in case it helps you troubleshoot yours.
Good luck