Best guess would be, that the carbs need to be 'freshened up' , new rubber parts, gaskets, floats, float needle valves, as the bike is 29 years old .
All the passageways in the carbs new to be cleaned with carb cleaner to assure that they are not restricted .
Also on the carb bowl, there is a small reservoir in one corner, at the bottom is a small hole in a brass fitting, not uncommon to have this get clogged and the bike won't idle because of it .
Also, I would get rid of the old fuel, I let a bike sit for about a year with a full fuel tank with stabilizer and the fuel was pretty much no good anymore .
I'd remove the fuel tap from the fuel tank try to get all of the old fuel out, check the condition of the filter screen that goes over the fuel tap inlet tubes .
Replacing the fuel lines would probably be a good idea, they are most likely original, 29 years old .
These bikes need a bit of care after being idle for a few decades, once you get them back into shape, they will run for a long time, they are not high tech finicky machines .
My '82 LS started doing this about 2 months ago, parked it until my vacation (now), rebuild kit should be here Monday or Tuesday of next week .
I'm doing a complete rebuild, so I don't have to do this for another 20 years !!!!!
