***Edited based on posts below - sketch removed, refer to the modified one that Richard posted below**
In an attempt to simplify the matter, I put the attached diagram together.
In order to troubleshoot this effectively, you need a volt meter with a basic working knowledge of it.
Here is a sequence of events of operation:
1. Fuel level normal, ignition switch moved to run, but not crank. Power through the 7.5A fuse through the relay coil (with parallel resistor wire), through the thermistor to ground. Because the thermistor is covered with fuel, it dissipates the heat developed by the electrical current passing through it to ground 29, and the thermistor resistance is low (relative term). It is low enough that the voltage drop across the resistor coil is enough to pick the relay up. This opens the relay contact, and the light is out.
2. While cranking, the power to the 7.5A fuse is off (so that all available power is available for the starting load). The relay drops out, the contact returns to the normally closed shelf state, and power from the starter relay makes its way to the low fuel light through ground 57. This is the "proof out" circuit that confirms the bulb is good.
3. When cranking is done, and engine started, the key returns to run. We are back to step #1 and the light is out.
4. After driving, using enough fuel to expose the thermistor, there is no liquid heat transfer to remove the heat developed by the current passing through it. The thermistor heats up, and by its nature the resistance increases. There will be some time for this to occur, but I'm guessing perhaps 10's of seconds, not minutes. Once the thermistor resistance increases enough, the voltage drop across the relay gets to the point where is not enough to sustain it, and it drops out. The relay contact swings back to the normally closed shelf state, passing current through power from the starter relay through wire 366 to the low fuel light, to ground through 57.
I do have plans within a few weeks to do a functional test on my car. I will document the voltage levels (over time) of wire 367, which is key.
What I would recommend for you is this:
1. Measure from wire 366 to 57, and wire 365 to 29. Pull the connectors and probe the pins. With the key on, 365 to 29 should be 12V. With the key in "crank" position, 366 to 57 should be 12V If neither of these hold true, fix this problem before proceeding.
2. With previous disconnected plugs connected, turn key to crank. Low fuel light should come on. If it doesn't, fix this before proceeding.
3. Put key to run. Disconnect plug in trunk to thermistor. Temporarily jumper wire 367 to a clean ground. Low fuel light should come on. If it doesn't, fix this before proceeding.
4. Up to this point we have checked everything EXCEPT the thermistor. With the thermistor disconnected, measure resistance of the thermistor, from wire 367 to 29, on the harness that goes to the sensor. Report in a reply to this post what you measure.
5. Connect everything back up, and figure out a way to measure wire 367. One option is to stick a small needle through the insulation and attach the voltmeter to needle, with reference to a clean ground. Measure the voltage when the thermistor is covered with water, and then measure again with the thermistor exposed to air, waiting about 1 minute. Report these voltages back a reply to this post.
