The FSM lists a 0.5 volt drop (from the battery) as the test for good voltage at the solenoid. Yes, it'll pull in lower than that but you need to realize that once it does pull in and send 100s of amps to the starter motor is that the battery voltage will drop lower. So if you are at the lower limit of pulling in the starter solenoid then it may drop out once the contacts close and send current to the motor.

Solenoid does pull about 20 amps per my measurement. So that is about like turning all your lights on and off.

r.c.brown@ieee.org
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