I'll take a guess just on a basic cap v. emissions/safety cap.
White housing: My thought is both emissions and addressing tip-over. The heat is going to expand and having a cap with a hole only like a lawnmower, those used to cause the vapor/heat to expand out of the tank and you'd also lose the knock agents along with the gas vapor. So emissions wise, this took a ball and spring times two. So think of a ball on top of a spring; this will be pulled down via vacuum and also the tip-over keeping the gas in the tank.
The other ball is on the bottom, with spring on top; this is for expansion and blows off into a tube in the tank, dumps in a charcoal canister, and now is exposed to the air via emissions loop... kind of. I left out a more technical flow from tank to intake manifold and help burn the overflow, like say at the gas fill, top it off too much/too late, and saturate the canister and how you address that... with the fuel heading down that tube in the tank.... if applies.
So if you don't care about tip-over on a hot(er) pipe near the head and torch the bike, just blow in either hole you can see. Suck it back and it should flow both ways = Not the cap.
Cap with balls and springs, the theory is either it sucks or blows both ways on the flip of holes. If they match blow for blow v. blow no blow, has to blow no blow to work, right? Where no blow is tip-over side. Blow for blow, tip is disabled.
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Sensor wise, I would look at it as a heat factor. Meaning, it reaches a point of max heat and fails, then comes back online when cooled.
Fuel loss or falling on its face [vacuum] at heavy loads and never losing spark is fuel flow.
Carb-Tree flow of jobbers:
a. Cap = vac.
b. Petcock = clogged/no gas.
c. Fuel line = kinked/internal bubble of material leaving wall and closing flow.
d. Carb = Needle stuck/float level.
FI:
a. Fuel pump = Low pressure at the pump.
b. Fuel line = Internal bubble of flex line/steel line crimp.
c. Injectors = spray holes clogged/plunger losing magnetism to retract needle and expose spray holes.
WOT I miss?