I don't know a damn thing about your engine, but if your explanation is correct the solution seems obvious. Either keep the tank full or replace the shorter tube with a longer one.

I think you have the Pulsa-jet engine, a horizontal shaft engine, with the carburetor that is bolted at an angle to the side of the cylinder, and it also has the fuel tank under it.
If so--go to the lawn mower repair shop, and buy a fuel pump gasket for it. Remove the side plate on the carb, and carefully blow out the holes in there. Install a new pump gasket and bolt it all back up.DO NOT HAVE GAS IN THE TANK FOR THIS! YOU WILL GET A BATH OF GASOLINE! AND WATCH HOW IT GOES BACK TOGETHER! You don't have to remove the carb for this work! Spring in first, then hollow cup, then gasket, then the cap and bolts.
When you get that part fixed, then make sure the tank is full enough to allow the small pan inside the tank to fill up so the carb can suck it in! This is only a one time deal. Next time you go to use it, you'll probably have to fill the tank again, if allowed to set too long.

Thanks Rusty, that helps!