Carb sitting over a year. Was it cleaned or did you ever remove the gas from it on teardown? Try what Mike said, then when it starts to die out, turn the petcock back on, watch the gas leak out again. Pull carb.
Carb overflow troubletree:
a. Petcock is closed but leaks when turned off.
b. Debris is stuck between needle and seat... what Mike said so the gush of gas can flush that out is the one variable mentioned.
c. Float hinges varnished onto the float pin and is stuck.
d. Float needle [if rubberized] cannot hold close the flow.
e. Seat to needle both worn and still flows with proper float level.
f. Float level off at adjustment level.
g. Floats made of brass can fill up, to saturating a fiber type bowl and that weight keeps the flow going.
Sometimes the gas remains [at the bottom of the bowl] on engine off, clogs the main jet... being that deep still submerged in the soon to be varnish.