Always give year, make, engine size and model # when asking questions. We need all of that info to give an informed answer.
Depending on the year, some Vulcan 750s had a problem with the pulse coils (on the engine down by the flywheel) shifting their position which would affect the ignition timing.
Shifting gears will change the RPMs of the engine which will alter the timing advance at the moment.
The "air gap" of the pulse coils had to be adjusted.
Edit
Before getting to involved with electrical trouble shooting, check mechanical things first.
Adjust the valves - it's probably never been done.
Remove and clean the carbs - dirty carbs could gum up the throttle slides, preventing them from raising smoothly.
The throttle slide diaphragms could be cracked or leaking.
Could have water in the gas.
Look in the fuel tank for rust (not good).
Check for intake manifold leaks - especially if the carbs have been removed.
Check for exhaust leaks at the heads and muffler joints.