I was writing backwards. I pull the enrichener towards me.
I didn't know about the Rocker Arm pivot bolt. I'll add it to the list. Thanks.
Too many people in-advertently or on-purpose will open the throttle while pressing the starter button.
The Keihin CVK carb does NOT have an accelerator pump and it does Not have a choke plate. The cold start enrichener opens a Separate jet & a Separate air passage, specifically for starting. Any opening of the throttle plate can Reduce or even Totally Negate the separate Cold Start enrichener system.
The fact that it fires once or twice is most likely because of the 'Accumulated Fumes' in the clean-side of the air box from over-night evaporation. Once their consumed the incoming air needs to be enrichened.
So I'll suggest that you keep your hand completely off of the RH grip & attempt to start with Full Enrichener & only your RH Index finger used on the starter button.
If this does not light its fire, it may be because of Low engine compression due to tight valve clearances.
When the RH exhaust is below spec or worse, nearing '0' clearance, the Kawasaki Automatic Compression Release hold that EX valve open too far Up the up-stroke of compression. Which remaining compression can dip below the recommended minimum of 77PSI.
With 11,000 miles on the bike this is a very strong possibility.
Always attempt to select thinner valve shims to achieve near maximum valve tappet clearance, but NOT loose on the thickest feeler gauge. Lightly snug on thickest or loose on next size or two under max is great.
Intake specs is .004 - .008 inches & Exhaust specs is .006 - .010 inches. The valve shims come in .002 inch increments. The ink marks face DOWN. The inks marks are in 0.05mm increments / .002 inch.