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To check a step down transformer that is not powered you set the meter to ohms a low range is fine , measure the resistance across the primary side and the secondary side, the resistance should fall closely to what ever the ratio was of the input and output voltages , so say the transformer is a 240 to 24, then the resistance will be ten times as much on the primary side, basically because it has 10 times the amount of windings in it than the secondary side. ( The current draw then goes up by ten on the secondary side ).
To check it while energized you check for voltage, if you have the rated voltage on the primary side you should then have rated voltage on the secondary side.
When power and control wires are disconnected it should give you an ohms reading , a low reading because it is an inductance load and the resistance will go up when it is energized. Basically if you measure anything but 0 or infinity it is more than likely a good coil. The typical reading is 20 ohms.
If you get a good ohm reading and have the rated voltage on the coil there then the plunger is probably stuck or not working.