The airplane has a fairly simple fuel system. At least, I've seen worse. The fuel sits right in the wings, no fancy tanks, no bladders, just fuel everywhere, with the ribs acting as anti-slosh baffles and the five percent dihedral directing the fuel inboard. Yup, it leaks. There are flapper valves on three of the ribs to allow fuel to flow inboard but not outboard. Inboard of the engine nacelle, at the wing root, the inside of the wing is divided along the the chord into three sections: a forward collector tank, a centre hopper tank and an aft collector tank. Two submersible boost pumps are in the fuel in the hopper tank and the tanks are connected to each other and the main body of the wing though flapper valves, allowing fuel into but not out of the hopper tank. The boost pumps (only one per wing can be selected on at a time, so they are used on alternate days) send the fuel towards the engines, but on the way there some of the fuel is diverted down a side line to provide the motive force for a pair of jet pumps (the same as ejector pumps, look it up) to transfer fuel from the collector tanks to the hopper tank and always keep the hopper tank full to its fourteen gallon capacity.
Further downstream in that line is an electrically operated emergency shutoff valve, a filter, with a bypass line in case the filter gets plugged, a fuel heating loop through which an anti-icing valve will automatically meter fuel if need be, a fuel transmitter, engine driven fuel pumps, a fuel control unit, and the engine. There is no crossfeed system, but there's an electrically operated valve you can open that connects the two wing tanks through a pipe, and you can transfer fuel through it by sideslipping, or balance the two sides (they have to be within 500 lbs) by remaining in level flight with it open. Sophisticated, eh?
Fuel indication is through capacitance, with five capacitance probes in each tank. The cockpit fuel gauge reads in pounds and is corrected to read zero when only the thirteen pounds of unusable fuel remains. For reasons I haven't researched, failure of one of the probes causes fuel quantity to overread on the gauge, which requires 115V AC power for its operation. There is also a float switch in the hopper tank which illuminates an annunciator whenever there is less than 13 gallons in the hopper. The annunciator is labelled L/R XFER PUMP, because one reason for there to be less than 14 gallons in a hopper tank is that the corresponding boost pump failed, so the ejectors aren't transferring fuel from the collectors, and there is less than 600-700 lbs of fuel in the tank so that the hopper doesn't stay full anyway. If you turn on the other boost pump in that tank and the light goes out, then you had a bad boost pump. If the light doesn't go out, then it means one of
(a) you have two bad boost pumps and less than 700 lbs of fuel on that side,
(b) the boost pump is working and you have less than 75 lbs of fuel on that side, or
(c) the flapper valve that triggers the XFER PUMP light is stuck.
Option (c) is by far the most likely, and can be verified to near-certainly by knowing how much fuel you put in the airplane and crosschecking with the fuel gauge and the fuel flow totalizer. If no boost pump is working in a tank, the unusable fuel increases to 88 lbs, and the usable fuel will have been exhausted when the gauge reads 75 lbs. Because AC gauges freeze in place when power is removed, there is a test switch on the fuel gauge. When the test switch is depressed, the fuel gauge should indicate zero, if it's working correctly.
Here's some more about the boost pumps. The two pumps on any one side are exactly the same as far as I know, but one is called "main" and the other called "aux," just so you can tell them apart. The switch that controls them is a vertically mounted three position rocker switch, OFF in the middle, MAIN on the top and AUX on the bottom. For each wing the main pump runs on 28.5V DC electric from the corresponding essential DC electrical bus, and the aux pump draws power through the opposite bus. That way, with one essential bus failed, you can still have one operating boost pump in each tank.
There is a gauge showing fuel pressure between the engine-driven low and high pressure boost pumps. It requires 26V AC power and should read 20-30 p.s.i. while the engine is in operation.
And in case you're wondering, yes I am going to just spew airplane systems at you for the next little while. I'm writing multiple ones a day, so they'll last you a couple of weeks. This is what I have to know and do in order to get to the point where you're pushing the throttles forward. Feel free to e-mail me random quizzes on what I profess to know.