Agree that pretty sure the 10th character in the 17 character VIN is the model year, but to be honest, the exact year might be of little consequence because it's unlikely Kawasaki will still be selling parts for a 1980's motorcycle, so that leaves you having to buy used parts or aftermarket bits which is seldom the same thing. Add to that you are likely to encounter some difficulty registering a motorcycle with unknown history, unless you are building a race bike, you might want to try to plate the bike asap to determine if that is possible.
On the carburetors, the best carburetor parts are usually the original ones and most of the problems will be in the bottom part of the carburetor where the fuel has evaporated out and likely to have plugged up the emulsion tube and jets. Clean the carburetors correctly and your fuel problems are almost certain to go away. Buying parts before you even look at the original parts is usually a great way to waste money.
On the carburetors, the best carburetor parts are usually the original ones and most of the problems will be in the bottom part of the carburetor where the fuel has evaporated out and likely to have plugged up the emulsion tube and jets. Clean the carburetors correctly and your fuel problems are almost certain to go away. Buying parts before you even look at the original parts is usually a great way to waste money.