If I understand you right, you might not be in as bad a shape as you think. When you say you connected the positive of the LED to the battery circuit, do you mean you connected it to the *positive* lead from the battery? If so, then really 5 and 6 were sitting at the same potential. Not right, but not necessarily fatal.
——-That’s a good point. That’s exactly what I mean. Positive was hooked up to positive so I guess they were sitting at the same battery voltage. ——-
I'd recommend troubleshooting in a logical sequence. First, jumper 6 to 7 and see if the pump runs. If it doesn't, then the problem isn't in the relay or controls.
——Pump runs good without this module. When removed from the set up, it turns on and off with the switch perfectly and runs strong. ——
Next, as dogdog states, you should have 5v at 11. If you jumper that to 2, does the pump run? There is some delay/hysteresis, what this sheet calls debounce. That means it might take a minute or so before the relay engages and the pump turns on. No worries, just take note of the amount of time. All subsequent tests have to hold that condition for at least that long.
—I am getting 5 v at 11. When I jumper 11 to 2, I still get no power on 7. Held for several minutes.
Next, with the sensor connected do you see 5v at 2 when the sensor is submerged in fuel? Voltage should drop when pulled out of the fuel - might not go to zero, but it should certainly be less than 2v. Depends on the sensor.
Submerged in fuel with sensor hooked up = 3.75 volts.
Good luck, let us know what you find!