You're thinking in the right direction, just back up a little. I don't know your machine, but many of the small mills have a switch on the speed pot so the machine always starts slow. Lacking that, use the On/Off switch. A good place to look for a switched lead is to trace the center tab from the fuse holder. Follow that through any switch, then attach a 120 Volt hourmeter. The switch may be ahead of the fuse. Any 120 Volt line that is switched should work. Any neutral will do, from the line cord follow the white wire to a common tie point. Inside the control cabinet, with it's short runs, pairing the two wires doesn't buy you anything. Finding a place to mount the meter will be the biggest problem. If you need to use an external mounting, be sure to use an enclosure rated for line voltage, and the pass through hole is smooth.
You should have a multi-meter, make sure the wires used are switched 120 Volt AC leads. Machine time is the same as On time. The spindle doesn't need to be turning. 120 Volt hourmeters are common, be sure not to use a low voltage or DC type. There is DC in the machine, usually PWM (Pulse Width Modulation) for a small machine. That DC signal has a very high switched frequency and is NOT suitable for anything but the motor. It may well will be higher voltage than the line.
The machine must be powered on when the cabinet is opened. Be sure to unplug it before reaching in for any more than a voltage measurement. Electricity is dangerous, that is well known. Be sure to have a clear work surface when the controls are opened. For a novice, even 32 Volts can put you down. Be sure to have a way to lay the front panel down so nothing touches.
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