2020 dies when less than a quarter tank

[J-bear]

I have a 2020 gas. When the fuel gets below around a third to a quarter tank, the engine will sputter for a few seconds and die, especially under load. It will usually restart and run for a few seconds and do the same thing. It will keep doing that until I fill the gas tank up, disconnect the fuel supply line at the carb, and crank the engine for 10-12 seconds (dumping fuel onto the ground). Sometimes I have to do the disconnect and crank routine a couple of times before it stops the sputtering, then it runs like a top until the fuel gets low in the tank again. I don"t think it"s the carb, as I recently had that rebuilt and it runs perfectly until the fuel gets low. I thought maybe the fuel pump is starting to go bad, so tonight I pulled that off and cycled the lever with my thumb over the intake port. It seemed to be generating good suction (I could hear a tiny "pop" when I pulled my thumb off).
There has always been some wetness on one of the connections where the fuel line connects to the pump. I"m guessing that the tiny leak was letting air into the line, preventing the pump from pull enough fuel when not aided by gravity when there was enough fuel in the tank?
Any other ideas?
 

[Cliff Nelson]

Repeat the fuel pump test with your finger over the outlet port. Should be pressure there. there are two check valves in the pump and you only tested one of them. Your symptoms indicate a bad fuel pump.
 

[MSD]

Bad fuel pump!
 

[David G]

Fuel pump, $35
 

[Jim Skala]

I bet the fuel filter right before the carb is partially plugged up with dirt.
 

[buickanddeere]

Fuel pump and filter.
The filter is hidden in the gas line elbow.
 

[Tx Jim]

T19743 FILTER,GASOLINE FUEL ADD 12.87 USD
RE43274 PUMP,FUEL TRANSFER,ASSEMBLY ADD 82.79 USD