I don't think it is an MOV.
The photo is clear enough to show that the mains comes in from the connector at the bottom left, and goes from there to the transformer via the black wires. The transformer output, 24 V ac, goes via yellow wires to the bridge rectifier, the square component bolted down in the bottom left of the box.
Bridge rectifiers like that have ac input on opposite corners, and the dc output on the other diagonal. The ac inputs on yours seem to be top left and bottom right of the bridge rectifier, and the dc outputs are top right and bottom left.
The mystery component appears to be connected between one of the dc outputs and the connectors on the box, and it seems to be in series with the load. I think that makes the mystery component either a PTC or and NTC thermistor.
A PTC thermistor is used as a self resetting fuse. PTC stands for positive temperature coefficient, and the resistance will increase as they heat up. If too much current is taken, the thermistor gets hot, its resistance increases and the current is reduced.
An NTC thermistor is used as an inrush limiting device, maybe used as a soft-start. The idea is that there is some resistance in series, to limit the current at start-up, but after that the NTC heats up and its resistance drops allowing full power through.
I am not sure which is used. I would think that the PTC is more likely. Either way, the voltage across the mystery component should be less than about 1 V when running.
https://www.farnell.com/datasheets/1902602.pdf shows some. I have no idea what the rating is.
If you want to fault-find, take lots of photos to make sure you can put it back. Then disconnect the transformer from the bridge rectifier. If you connect the mains, the output of the transformer should be around 30 V ac. To test the bridge rectifier, find the ac connections, labelled "~" and the dc connections, labelled + and - . If you connect a voltmeter, set to dc to the dc connections, and connect a 9 V battery to the ac connections. The voltmeter should read about 1 V less than the battery voltage. Now reverse the battery, and the voltmeter should read the same.
If those are OK, put it back together and turn on. Measure the voltage on the output. It should be around 30 V dc. Now connect the motor. If it doesn't run, and the voltage across the mystery object is more than 20 V, try connecting an ammeter in parallel with the mystery object. If that makes the motor run, it looks like the mystery object need replacing.