I have this same problem and was thinking this may be. Shouldn't it hold vacuum for at least several minutes? So it could be the vacuum solenoid on the passenger fender, the vacuum reservoir and/or the vacuum lines?
I had several vacuum reservoirs that developed leaks.
Usually the seam.
MY truck now doesn't have one at all.
the Last EGR 2.9 I had is several years in the past,
the Non-EGR 2.9's I had only had vacuum lines
between the FPR and the intake manifold
and between the manifold and brake power booster.
And since switching to a 4.0 I actually added a vacuum line...
To the air intake vacuum pot for the air preheat
(TB icing can be a real bitch)
and since I have an '87 cab all of the HVAC controls are mechanical
(cables), so I don't have a blend door vacuum actuator like a gen2
either.
How loud is this buzzing?
AD