Suzuki vinson 500

Yes check under the seat on the starter solenoid
there is a fuse there for the starter

Take the bike to a PROFESSIONAL...this is too good a bike for a amateur to "play mechanic" on!!

sounds like weak fuel flow. something blocking it or ???. it'll run off the carb bowl for a while.

This is the drive system for your quad... it take all the engine power and transfers it to the rear wheels,, its going to get hot,, If it starts smoking real bad... and smells worse.. drop by your local Suzuki dealer and talk to the service manager,, get his opinion.

Sounds to me like a battery and/or charging issue. But could be a loose connection somewhere too.

Although the symptoms you have described are those of a low battery, there are a few other things it could be.
First, have the battery tested to see if that is the problem.
Then, take apart and check the starter solenoid to see if the copper disc is burned and needs to be cleaned and lubricated.
Also, then take apart and check the starter motor, to see if it needs to be cleaned and refurbished.
God bless your efforts.

This is a download. See if it is what you are looking for. 2005 Suzuki Vinson Service Manual

I assume engine is still running but losing drive. Simplest thing is
belt has worn.

water in the transmission? drain and check fluid

Check all the easy things first gas on reverse ..is it in gear ..reverse handle is not hitting ? Hope it helps ..