Motorcycle Repair: dead cylinder and backfiring, vacuum tubes, air leaks

Question
Hey Wayne,
I'm very confused about a problem with my vintage 1980 GS750 and hope you can help. When I start it, it takes about 5 minutes or more for #4 pipe to get hot while the others are hot almost immediately. Eventually, it gets as hot as the others, I think. It also backfires upon deceleration on the right side, which I assume is because of #4. This occurs even at full heat. Here are the things I know for sure:
1. It actually runs quite well, otherwise. It accelerates great, starts easily, idles smoothly and doesn't seem at all rough.
2. The carbs are perfect inside and out. I am very good at rebuilding them and have done so in the last couple of weeks. I always put in new "O" rings and do a thorough job.
3. The bike has 20K easy miles on it, has no air leaks, no pinched vacuum tubes, is totally stock and is getting plenty of gas to each carb.
4. The valves are adjusted perfectly and the compression is great.
5. The plugs are new and look perfect (light tan)...even #4 which really confuses me!! (I've adjusted the mixture screws correctly.)
6. The coils test perfectly and I've switched #4 and #1 with no difference in "cold #4). All plugs are getting a nice spark. The signal generator also tests great. As you know, I have electronic ignition.
7. The carbs appear to be perfectly synched (I use Carbtune, which is a really nice set-up.)(I don't know why #4 isn't goofy!?!)
I'm sorry to make this so long but I don't want to leave anything out. When I adjusted the valves, some clearances were fairly tight but everything looked to be alright. What in the world do you think is causing the cold cylinder and the backfiring?? I'm absolutely baffled, especially since the plug looks to be very "healthy". Thank you, very much, for any advice you can offer!!

Answer
Brad,

-is the choke or enrichener plunger worn
and the brass pickup tube okay in the carb?

-When cold does the idle speed change if you pull
the plug wire off #4 cylinder?
-If it doesn't then the cylinder is not
running. See if the engine speed changes
putting the wire on and off at cold idle.

-If the speed changes, it must be running.
The amount of fuel it draws in is related
to the vacuum the cylinder has.

-if the speed does not change it must not be
running which indicates a loss of vacuum
when cold or choke/fuel problem.

-try choking that cylinder slightly
by partially blocking the air intake.
See if it helps. Then you know it
is a vacuum/fuel loss.

-try setting the sync so the vacuum is lower
on that carb. (speed that carb up slightly)

-get the cylinder tested for leak down
as the piston is raised and lowered,
this will expose any vacuum or compression
leaks further down from TDC in the cylinder.
-There may be a vacuum/compression loss
that only shows up when the engine
is running.