Two carbs getting gas, two do not.

You need to be careful when installing the bowls.  Sometimes the float will get stuck on the side of the bowl.

I would remove the carbs from the bike and remove the bowl from #2 carb.  Attach the tank and see if fuel flows through the float valve.  If it does, then reinstall the bowl, remove the drain and try running fuel again.  If it doesn't then check your float valve for a blockage.

Do you have a vacuum petcock or is it simply gravity fed?

Wookie58 wrote:

Have you tried removing the float and needle assembly, put the bowl back on and turn on the fuel - does the bowl now flood?
Yes: fault relates to the float or needle
No: fault is a blockage in the carb body

Further update:  This morning I ran the above test suggested by Wookie.  Surprisingly to me, all carbs got fuel.  (I was to the point of assuming that number 2 had a blockage).  So,  now it's trying to determine the problem with the float or the needle.   Progress!  Thanks Wookie!  All float needles appear to be OK. Should I replace them just to be certain?  What is the proper float height?  I'm reading 24 mm but am not certain that's correct.  

hardrockminer wrote:

You need to be careful when installing the bowls.  Sometimes the float will get stuck on the side of the bowl.

I would remove the carbs from the bike and remove the bowl from #2 carb.  Attach the tank and see if fuel flows through the float valve.  If it does, then reinstall the bowl, remove the drain and try running fuel again.  If it doesn't then check your float valve for a blockage.

Do you have a vacuum petcock or is it simply gravity fed?

It's a vacuum petcock.  (See my other post for a general update).   Another reply suggested that a tear in the petcock diaphragm could cause a fuel problem in carb 2.   Is this correct?  (I did rebuild the petcock including a new diaphragm)  

OK, so you're using the vacuum port on #2 carb to operate the petcock.  

Do you have a maintenance manual for the bike?  There is a section on how to decide if the float needles need replacing.  I've never seen the need to replace them.

I'm not 100% sure about your carbs, but mine are 1978 version and the correct height is 3.5 mm from the top of the bowl, plus or minus 1 mm.

Here are some of the carb tables from some FSMs which show both design and service levels for float/fuel level.

According to the info in the previous post your fuel level should be 3 mm plus or minus 1 mm.  Stated another way...between 2 mm and 4 mm.

Update:  After repeated attempts to get fuel flowing to carbs 2 & 3 I asked for help from a guy who lives nearby and makes excellent YouTube videos.  ( MotoResto Florida - YouTube
I found him totally be accident by watching several of his videos and realizing that he lives about three miles away.  Anyway, he looked at the carbs and quickly realized that the float needles on carbs two and three were sticking.  After replacing the float needles the problem was resolved.  Also, he helped me set the fuel level by using the clear tube method.  The bike is now running on all four cylinders.  The remaining issue is a mild backfire through the exhaust.  Ideas?  

This has been a good learning experience for a 75 year-old amateur motorcycle mechanic.  Thanks for all your ideas.  

Good to hear you got the fuel supply sorted, ref the popping in the exhaust - how old are your rubber manifolds (sounds like an air leak issue) ?

The rubber manifolds/boots on the carbs?  They are almost new.  I replaced the ones from the airbox to the carbs and the others appear in good shape.  
 

Backfiring back through the carbs is mostly caused by lean fuel supply, be it either an air leak or lean fuel air ratio settings.(which amounts to the same thing). 
Back firing through the exhaust is almost the opposite. Partially burnt/unburnt fuel is being pushed out the exhaust valve/s. Once the ratio of fuel vapour and oxygen reaches optimum, bearing in mind its mostly carbon monoxide in there, the next hot exhaust valve cycle ignites it. 
Finding the reason for unburnt fuel is the hardest part. Inefficient combustion caused by dirty/fouled/poorly earthed/badly gapped plugs or low voltage supply to the coils is the most likely cause. 

It was an air leak.  In my excitement and haste to get the carbs back on the bike and hear it run,  I failed to tighten the clamps on the intake tubes.  
Maybe it's senility, but I would never admit to that.  

Thanks again for all the ideas.  I'm not only pleased with how it's running, I'm happy with all that I'm learning.  

"All's well that ends well"