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To remove the choke cable from the carbs AND from the choke lever on the handlebars.Remove the small bolts on the carb first (then slide the 2 choke plungers out of the carbs) and then disconnect the choke cable from the lever on the handlebars last.
Easiest way is to remove the carbs and take the chokes out...there is 2 small phillips head screws that hold the chock bracket in place.. clean the area where the chokes go into the carbs with carb spray(I like B-12 Chemtool Carb spray) Then clean the chokes with carb spray.. after you get done, spray some WD-40 in the area where choke go into the carbs and then the chokes.. Also you may have to remove the choke cable from the handlebar lever and use WD-40 to flush out the cable housing.. Reinstall and make sure they are moving freely.
I FOUND OUT IT IS A VERY COMMON PROBLEM.THE PROLEM IS THE FACTORY SPRINGS ARE TOO WEAK.YOU CAN EITHER STRECH YOURS A BIT OR THE BEST CHOICE WOULD BE TO ORDER 2 CHOKE SPRINGS FOR A Kawasaki BIKE AND THEY ARE LONGER AND SINCE I INSTALLED THEM I HAVE HAD NO CHOKE ISSUES.
For more help and diagrams.
Go to Kawasaki.com and take a look at the parts diagrams for the carburetor and the cables to identify how they are constructed. Removal is a snap once you sort out the relationship of the two components involved.