Ok, let's give it a shot. I can help you diagnose it, but know that I can't teach you how to be a mechanic
Please read
carefully, follow the order, and remember that YOUR answers will be the key to finding the issue. Details matter, I'll try to ask yes/no questions. So, let's try a couple simple things to narrow it down and see where it leads us next:
Disclaimer: These are generic tests I am doing over the internet, sight unseen with damn near zero information. NOT Buell specific, and I am an idiot.
These tests check the safety systems of the kickstand/clutch/neutral switches as a group:
Does your neutral light work correctly? Neutral switch/wiring is bad, fix it and we're done! Yay that was easy! Oh wait it does work? Ok then, theres more.
ATTGATT. Clear path forward. Get on the bike. Idling, kickstand DOWN, clutch IN, select 1st gear, does it die? Clutch or kickstand switch/wiring is bad.
If it's still running, be prepared for the bike to move forward and let the clutch OUT s.l.o.w.l.y. Does it die immediately (like shutting off the key)? Clutch switch/wiring is bad.
Or does it start to pull forward a bit then chug/chug/stall? Safety switches are fine, now checking carb:
Put the kickstand UP, re start it and try to waddle forward with it using no throttle, until the clutch is fully OUT and you're moving down the road at idle. Fuel supply is OK.
Once you get it idling in gear and moving, open the throttle a
slowly, does it stall? No, It just keeps going a little faster? Main circuit is clogged.
Go back to just idling forward (clutch still fully OUT)
and be prepared for a stall while moving!!! and open the throttle hard, does it stall now? Accel pump is clogged/inop.
If you can get it to repeatedly fail one of those tests, you'll have your answer.
*My total clairvoyant guess is the clutch or kickstand switch is bad.