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If it were mine, I'd attach a meter to the two ends of the resistor with alligator clips so I could read the voltage across it without having to get to it with probes. (You probably already did this.)
To cause that resistor to overheat so much that it make a popping sound in a few seconds...
The resistor has to dissipate about 24² ÷ 56 = 10.28 watts. It does this only when the switch is held in the start position. It's rated at 25 watts when properly mounted to a heat sink. It can handle 10 watts intermittently as it needs to in this application without being mounted to a heat...
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