Colin
I have the same lathe as you. I have taken a photo of the opto sensor board and measured the voltages.

As you can see, the cables are marked with a '+', a dot and a long dash (left to right) . I have confirmed that they are + 5 volts, ground, and output (left to right again).
Output is about 5 volts when power is on but lathe is not turning. ( the output is biased to 5 volts by a 10 k resistor on this board.) It is pulled down by the sensor when detecting pulses. With the lathe turning, I measured the dc voltage using my multimeter and it was about 2 volts and dropped as the speed was increased. This would be a simple check if you don’t have access to an oscilloscope.
There are 2 resistors on this board. The top one ( nearest the sensor) is 10 k and is connected between + 5 volts and the output to bias the output high ( ie to 5 volts). The bottom one is 300 ohms and is the current limiting resistor in the feed from the 5 volt supply to the LED of the sensor.
I don't know if this is any help, but at least you will know what to expect at this board.
I don't think that the diagram posted by Steve earlier can be the power supply circuit for this type of speed sensor as this would not provide enough current for the LED with a 10k resistor in circuit.
I am going to be dismantling my lathe in the next few days to change the gears and bearings, so if you don't resolve the problem by then I can measure the volts and take some photos on the circuit boards on mine.
Stuart