In the experimental world, several of us are using a tapered header tank, WITH a sight gauge. Both wing tanks plumbed direct to the header, no shutoffs between. One outlet in each tank.
The way it works, I'm told.... is you fly along until the right wing tank sight gauge shows empty, as that tank always empties first, it is of no concern. Then, you start watching the left tank's level, and about 30 minutes after the last of the visible fuel disappears from it's sight gauge you starting looking around behind you every few minutes (or seconds, depending on the terrain, WX, and amount of fuel remaining) and now when you see the gas level start to drop in the header, and assuming you're flying behind a Rotax 912S, you still have 1 hr to 45 minutes of flight time left. The header holds 4 gallons. The taper of the tank is such that some report flying along (and taking off) with only a gallon OR LESS in the header, but, they knew exactly that that was the situation, no guess work about how much fuel was sloshing around in the mains or how accurate the electric gauge was. The end result seems to be more range, one guy flies 8 to 9 hrs between re-fueling with this setup, resulting in far less fuel stops, just due to the total awareness of the actual fuel remaining. In a real pinch, when some are cutting it real close, like sub 1 gallon remaining, the observed fuel remaining in the tapered header drains quicker and quicker, as the tank volume is less so the fuel seems to drain quicker, this visual effect must be allowed for or it will cause severe consternation they say. When the last of the fuel in the header is gone, there is not a drop left in the airplane anywhere, so at least the resulting deadstick landing probably won't result in much of a fire.