That's normal unless you're trying to start the engine. Connect the negative lead of the voltmeter to the negative terminal of the battery. Confirm 12VDC at the "input" side of the solenoid and 0VDC on the "output" side. Now make the solenoid "click". If you don't see 12VDC on the "output" side while trying to start the engine, the solenoid is not functioning.
Did you get a spark? Anything at all?
Presuming you have a multimeter that can measure resistance (ohms), try this: DISCONNECT the battery's negative cable. Then measure from the solenoid's "output" side to the (disconnected) negative battery cable. This will measure the resistance of the starter windings. You should see very low resistance (almost a short circuit). If you see no continuity at all (open circuit) or high resistance, there is a problem with the starter and/or the power cables connecting to it.
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