Hi there – and welcome to the board ……..
It does sound like a carb problem – and for reference, you can find a variety of manuals here Service and Repair Manuals
“If” the carb isn’t set up correctly, the amount of fuel going into the engine will out strip supply, running the float bowl empty. Once the engine stops, the float bowl continues to fill, until you start her up again, when once more the engine uses up more than is in the float bowl – rinse and repeat.
There could be a variety of reasons for this – blocked holes everywhere – float level incorrectly adjusted etc – but as someone else has worked on that carb you now have consider the area to be highly suspect – which means checking everything from scratch.
Before you strip the carb down – have you tried sea foam (we call it Redex over here) in the fuel ? This will sometimes shift the blockage, but needs to be tried and run for a couple of days to work properly. You may also wish to use a fuel filter in between the tank and the carb to stop any future contamination confusing the issue.
Should it turn out to be a carb strip down situation, there are a lot of little bits in there which need to be assembled correctly – don’t presume that the last person in there got everything the right way around - we’ve had a few instances of faulty re-builds being replicated. Proceed with a high level of suspicion – after all – it doesn’t work now, so if you re-build it the same way, no prizes for anticipating the end result. The carbs on these bikes are quite small, so even the slightest deviation will stop them from running properly.
It will help a lot to state the exact year of TW, in order for others to chime in in future – there are a lot of good people on here, but we need to know what we’re dealing with …………..