Dying out after warm?? (20 to 30 min)

So my 78 KZ1000 Ltd has been giving me issues and I am stumped. I'd like to have an idea of what I am dealing with prior to going to the mechanic. So I start her up and and can ride decent like regular then after 20 minutes or so it just dies out and wont start. Then after letting it sit for a while maybe 30 to 45 mins she fires right up. I thought maybe the plugs were getting flooded and needed to dry out or possibly it is getting too hot and needs to cool. Totally lost, I appreciate any help you fellas can offer. In pic I was im"patiently" waiting to get her restarted...

Could be old coils overheating.
Could be fuel starvation caused by an automotive fuel filter, clogged tank vent, kinked fuel line, et cetera.
Why do the fuel lines curve upward as they come out of the petcock?

I don't think it is fuel because after sitting a few minutes it fires right up and starts quickly anytime it is cold. It is when hot that I seem to have issues.

I’m with Tex here. Fuel starvation or loss of spark. Does it sputter and die, that would lean toward fuel. If it just dies it might be spark. Could be coils, but hard to say both coils would drop out at exactly the same time. If it’s not sputtering and dieting from fuel starvation then It could be power to coils through a bad connection that builds heat and stops flowing current. Stock ignition or newer electronic? There is a vent in the tank cap. Remove the 3 screws and ttake the cap apart and make sure the vent is clear. Take a rag and flat blade screwdriver with you on your next ride when it dies CAREFULLY place the rag under the float bowl and just crack it open and see if fuel drips out. I have never heard of anyone test riding with a spark tester in place but I guess it’s possible to do. Is it possible it’s a 1979 with a resistor in the coil power circuit? 

 

 

what do your plugs look like after it dies?

If its got electronic ignition it could be one or both of the pick ups starting to heat fail. 

Thanks gentleman I will go through all of these possibilities, before sending her off..I have ordered a new gas cap and new electronic ignition as well as a new petcock just to be safe, actually found a black one....