We already discussed a option for checking to see if it's getting fuel. But he did say he was getting smoke which is really fuel vapor when he pumps the carb when it's hot. And when it cools down he can see the accelerator pump squirting.
And in some of this you may not have read but I did recommend a little squirt bottle of gas the next time it does this to put a little touch in the carburetor and see if it fires... This is what's leading the discussion to electrical... Fuel is way easy to verify... Without buying pressure gauges and all that...
