TOPIC:

I have read all your comments.

I rule out the tank breather because when it stops the first thing I do is open to see if there is fuel (that should equalize the pressure at least for another long time). As hardrockminer says, the issue is that both cylinders fall at the same time (both carburetors out of fuel simultaneously, weird thing), that was the first thing that made me think of the electrical failure

The Tytronic ignition cannot be the problem because I have recently installed it replacing the points and the problem is the SAME in both cases.

As for the coil needed, from what you say it seems like 4-5 ohms is good for points and 3 ohms for electronic ignition, so I probably need the green coil myself.
I would ask you hardrockminer why you decided to go 3 ohm?

At the time I had two Z1B's with Dyna ignition directly feeding 3.8 ohm coils.  My KZ1000 was completely stock ignition...OEM electronic ignition feeding an exciter which fed 1.9 ohm coils with a ballast resistor.  Occasionally the KZ1000 would have two cylinders drop out.  Since it was an intermittent problem it was hard to trace but I measured coil resistance and they were fine so I knew the problem was either the exciter or the 40 year old OEM pickup.  The options were to replace either the pickup, the exciter, both, or to go with the same setup as my Z1B's.  I knew options 1 and 2 might not solve the problem completely.  Only 3 or 4 would do that.  The cost was comparable so I opted for option 4 because it was simpler and it was the same as my other two bikes.  It also eliminated the need for an exciter.

I note that I mentioned earlier for you to check your coil resistance to see if that's where the problem lies.  If it's OK then the problem is either your exciter (if you have one) or your pickup.  

Correct, my coil also gives the correct value of ohms, but after a while it drops. I was left to check the reading in ohms at the moment of the drop, or to force this situation by heating the coil with a hair dryer.

What do you mean by "exciter"? with "pickup" I guess it's the coil. I am spanish, I have limited knowledge of English.

Apologies!  The pickup is the part that fits onto your crankshaft on the right side of the engine.  The exciter is a combination of rectifier and voltage regulator.  

Good.

The regulator and rectifier are new, I don't think they are bad. I also think that if they were bad, the rest of the electrical system would fail and not just the ignition.
I suspect your problem was fixed because (in addition to the other things) you changed the coil, but that's just a guess.

On the other hand I wrote to the ignition manufacturer Tytronic, with little hope. But he answered me. He says that for those ignitions a 3 or 4 ohm coil is fine.
So then those 3.8 ohm coils you use on your bikes will work for me. Are they the same green ones that you mentioned the other day?

Yes.  They are Dyna coils used on Z1 bikes.  They are not the same as coils for a 1980 KZ1000 because I modified the bike.

That is, you mean green coil model Dynatek DC1-1?
It says on the web that this coil is 3 ohms, but you say 3.8 ohms. Sorry for the extra-clarifications...

www.dynaonline.com/dyna-igntion-coils-se...g-single-fire-dc1-1/

I believe that's the one.  Send them a note to confirm the primary resistance.

Okay, thanks you for everything. Now let's see if I can get a loose one since everywhere they sell them in pairs hehe

I'll write again if this fixed the problem.

Finally I mounted the Dyna coil, which I don't regret because now the spark is magnificent, I think it would ignite anything I put in the engine lol

But it hasn't fixed the problem, so I think I have a fuel supply problem.

I have noticed that in carburetors one of the float bowls fills at a good rate, while the other fills much more slowly. I have unplugged the tubes coming from the petcock and one is spewing out a good amount of fuel while the other is giving out a weak stream. However, it is not clogged (the petcock is NEW), it seems to be a function or design problem.
When I mounted a plastic auxiliary reservoir, everything seemed to work fine.

I have to do more tests but it seems that I will have to put another petcock, I don't know if there will be better options.

Maybe a single outlet faucet with a T?

My apologies for ignoring those who told me about this from the beginning.