Vacuum Problems-345

["Joseph M. Shaw, II" <MikeIIDC@domain.elided>]

Help, Smart Guys!

About a year ago I began displaying my utter knack of knowledge and
mechanical ability on here when I was having an "overfiring" problem. 
Tore everything apart, tried everyone's suggestions, etc.  Finally,
after about six or seven months, Tom H. came down and helped me get the
thing running okay.  Didn't drive it much until quite recently-after I
wrecked my T'all.  It started doing the exact same thing after about a
month of regular driving.  This time it would go away-before it would
continue to buck and jerk for qas long as I would drive it.  It would
start this after about ten minutes of driving-after it had time to warm
up.
Anyway, I went to start with the easy things once again-Changed all the
plugs, wires, cap-then it got cold and I decided to come in.  I noticed
that the hose from the two pronged "outlet" fitting on the brake booster
drum was off.  The one on the bigger of the two stems.  I saw that the
plastic stem itself had broken off, so the clamp was still on, but the
hose had come off.  I reclamped the hose back on what was left of the
stem-enough to hold for now, I believe, then started it up.  There is no
hose on the smaller stem from this same fitting, and it is just exposed.
I had never had a hose on this opening, and assumed it had been plugged
in some way by the previous owner or mechanic or someone.  Well, when
checking to see that the other hose was on tight and not leaking I
discovered that this smaller opening was indeed "sucking wind" big time!
I looked around for any small hose that would attach to it and found
none, and from prior work, I know that I had never dealt with a hose
here, and I have played with the large one before.  Could this cause
what I am describing?  Would it only happen sometimes, though before
when it happened it did so with increasing frequency until it became a
constant.  This time it has started the same way and has been getting
more frequent.  Also, what would cause it to go away after a few
minutes?  Does anyone know where this should connect?  I found no other
openings anywhere that it should connect to-and my diagram on my air
cleaner does not really show it clearly enough for my pea brain.  What
is the formal name for the big "Brake Booster" drum on the driver's side
of the compartment near the firewall?  Is this the vacuum diaphragm? 
That is what it looked like on the diagram.  Also, this was a CA vehicle
that moved out of state and had its smog pump removed.  I am, for now,
just plugging this hole and driving to see if things are better.  Does
that sound acceptable?
Any input on any of these questions would be greatly appreciated!

Michael