Yes, it can be the relay. What I do is unplug the relay and swap it gor yhe horn relay. If this doesn't work, I use a volt/ohmmeter to probe the relay socket. Doing this, I can usually find the problem. With the key on , there should be two terminals in the socket that have battery voltage and one that is grounded. The last terminal goes to the pump and should show low ohms to ground. In your truck, the relay coil is connected to ground and turned on by the ecm with a positive signal. It also seems to depend on the oil pressure switch, so you might want to temporarily bypass the switch with a paper clip in the connector to see if that is keeeping the pump from running.
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