A voltage drop test is the displayed voltage when probes are on the same wire. Like terminal to terminal, with the circuit energized. Like pos battery POST to the POST on the starter. Displayed voltage is the drop. If I understand you correctly, you should have approx the same voltage, 12.3 at the blue wire. You are backprobing the jack? You did state the pump activates? If the pump activates, that shows the coil side of the relay is ok (most likely). If you have 12.3 at the brown, with the key in start and only .03 at the blue, it must be the relay, or a connection problem.