Those old style bailer bowl fuel valves are a curse on mankind. I bypassed them on two of my tractors after having similar issues on a grand scale. Funny I never had a lick of problem with either after that :thumbsup:. I can see now why they went away. Aside from that and before you do that go for the basics. Leaves and other **** in the gas tank. Stupid crap like that will drive you crazy as it displaces when you dump gas in then settle again later and you have fun all over again. The good news is you can look down in there with a nice bright light and see what's in there and siphon it out usually.
Don't think because those fuel passages in the filter bowl are open that fuel will flow necessarily either. If you see no leaves blocking the inlet take the whole assembly out and give it a good cleaning and blow out with high pressure air. I did have one so goofy that I finally drilled out the center completely and it still acted up till I ditched it in favor of a simple flow through. Try cleaning the passages and filter area, soaking in carb cleaner ect and see how it goes.
Having the silly little sealing ring at the top of the bowl slightly out of place caused me grief on my TO 20 also. It caused some sort of vapor lock so no gas would flow through. I had that happen a few times over the years. This always happened right after I pulled the bowl to clean out gunk.
Another BIGGY the gas cap. Is the internal vent plugged? Try opening of removing the cap and see if it flows. That can happen pretty quietly over time and you won't notice. Don't get fooled into thinking because the fuel bowl is full and clean that fuel is flowing, usually but not necessarily.
What about the carb itself? Pull the drain at the bottom of the bowl and gas should pour right out and keep flowing indefinitely. You can try removing the gas cap, screwing with the strainer, the sealing ring and watch down there and see if it starts or stops flowing so you really know whats going on. If you are getting gas and the carbs not firing try pulling off the rubber intake where it goes into the carb and spray gas into the intake while you start it or some starting fluid. If you can get it running on a spray bottle of gas keep it going and it will likely shake loose whatever is blocking the gas flow going into the carb bowl (if you ares lucky). If not then pull the bowl off the bottom and squirt it down inside and see if cleaning it helps. If not you may have to remove the carb, take it inside and give it a cleaning. It's easy and I never used a book . Also look at the float and make sure if its brass it doesn't have a hole worn in it and if composite it's not fuel soaked.
Somewhere in there you will find your issue. Like I said, POP THE CARB BOWL DRAIN. If you aren't getting gas then you will at least know when you solve it up above when the gas starts running out. It's always a good idea to disconnect the battery when messing with this stuff down there too in case you short across the starter ect. Good Luck.