Your going to need a volt meter to accurately test this. A test light is not going to do it. You have power right before the fuel pump but the light is dim so we do not know if the pump is trying to use that power and the circuit is low on amps or the circuit is low on amps prior to even getting to the pump. So far its looking like a wire thats faulty and has resistance or the pump has a poor ground. Use the diagram below if needed
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