You are correct. It appears they wired it wrong. Pin 5 should be your 12 volts and 4 is your ground. If you grounded Pin 3 then this is why your fuel gauge is not working because this is your primary signal wire. Pin 1, 2, and 3 all go directly to the BCM and are basically a 3 wire sensor that the BCM uses to determine fuel level. The BCM then takes this information and sends out over the CAN bus to the cluster to display. This means none of these three wires should be grounded. The BCM will handle this internally. However, if you added your ground to pin 3 I suspect you have an issue with your actual ground on pin 4 if this is what you did and the vehicle started.
So if the pump is not wired correctly then either rewire it or send it back and get another one. Then make sure your ground is good under the drivers seat. Worse case, run a new ground from the pump to a good location. Also, a lot of times you can't take those connectors apart without breaking them and if you break it they may not take it back so I would at least run it by the parts supplier and let them tell you to try it.
Let me know if you have questions.
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Wednesday, November 13th, 2019 AT 5:19 PM