TOPIC:

Sorry I will try to keep it to one thread. I will try running it with the gascap off. Thanks for the advice!

No problem, my apologies!

The petcock should have two hoses hooked to it. The larger diameter hose is for fuel and should connect to the fuel t between the carburetors. The smaller hose is to supply vacuum to the valve. On most KZs it connects to one of the carburetors. If the diaphragm inside the petcock is torn, it can allow too much air into the carburetor the hose is connected to, thus creating a very lean mixture. If the hose is cracked, the same problem will occur. If the hose is not connected, the lean mixture will be worse and the petcock will not work as designed.
The purpose of a vacuum operated petcock is to automatically shut off the flow of fuel when the engine stops. That is why there is no off position.

It's been many years but I do remember these systems. Triumphs and BSA's, Norton don't have anything like that.  I included a few pix of my fuel tap, carb and evaporative pump. On the vacuum diagram it looks like I need to tie the fuel tap into the black elbows on the carb sides and go to the evap pump 
 

Is that vac line on the side of the canister open to atmosphere ? The diagram shows it going back to the tank. This would effect the fuel petcock. How does it run with the petcock in the "prime" position?
PS: I fixed your pictures (when you have attached them click "insert all" before submitting) 

Thanks for fixing them. Everything is hooked up according to the diagram except someone had put in just an on/off fuel tap, so there's no vacuum line to the fuel tap. I need to rebuild it and "T" it in to the black elbows

If the manual tap works, and you do not mind remembering to use it, then there is no need to mess with the factory valve.

Ok damn it back to square one

Triryder wrote:

Went through the carbs, replacing floats and put a rebuild kit in it. ...
 

We're not familiar with the 305, but here's our few cents.

This sounds fuel related.

After replacing floats and, we assume, the float needle valves, was correct fuel level in the float bowls confirmed? We've seen aftermarket float needles cause fuel level to be way off from OEM spec. Aftermarket floats are a wild card too.

The carbs appear to be CV-type.  Were the slide diaphragms closely examined for tears / pinholes by gently stretching in good backlight?  Do the slides lift freely under gentle persuasion by finger, and return freely & smoothly by their spring pressure?

A longer shot:
Is full battery voltage present at the coil primaries?  Low primary voltage results in low secondary voltage = a weak spark. A weak spark that can jump the plug gap at atmospheric pressure, can "blow out" at the much-elevated pressure & turbulence at the top of the compression stroke.  In other words, more spark energy (higher secondary voltage) is required to jump the gap in a turbulent, pressurized environment than is required at atmospheric pressure.

Good Ridin'
slmjim & Z1BEBE

I wonder if something in that evaporative system might be hooked up wrong or malfunctioning in a way that causes a vacuum in the tank, similar to a clogged vent?

The device identified as the return pump would be high on my list of suspects. It looks like it could be hiding a one way valve or a diaphragm that after all these years could be malfunctioning. My personal inclination would be to remove them system completely to eliminate it as a possible problem.

Thanks for the reach out!  I thought it was fuel as well.  New floats from Kawasaki, New viton float needles, adjusted as per factory manual, or pretty damn close. The slides move freely and the diaphragms look perfect. I have brand new diaphragms from kawasaki, but haven't put them on because the ones in it look good. Plus not sure how to install them other then stretch the hell out them over the slides. And that can't be good. I can let it idle for 20 minutes, free Rev it and it sounds and revs fine. But soon as I pull the clutch in, and drop it in gear, that's when the problem start.  It will spit and sputter, I have to Rev high to keep it going and it will slowly lose power run worse then cut off.  Next time I start it, maybe a few hours later or the next day. Fires up and idles fine and free revs fine.  I tried running with the gas cap off, thinking vapor lock, nope.
 

Have you got a side stand switch? If so it's linked to the neutral light and clutch lever switch (although I don't know this specific model). It would appear you have 12v to the coils in neutral as it runs fine, rig up a voltmeter to the coils and see if it drops when the clutch is pulled, a gear engaged or the side stand retracted.