Wouldn't the brushes be sort of obvious? And usually I think the tacho generator hangs out the back a bit smaller diameter?

 

Wouldn't the brushes be sort of obvious?

Not in the ones commonly used in the early CNC servo's, the Tach was often a completely sealed unit that was coupled to the rear motor shaft. just two leads.
I still have a few left over in the 'junk' box.

 

OK, so we need for the TS to connect a voltmeter to the tach leads and spin the motor by hand to see what sort of voltage appears. An analog voltmeter will show a wiggle for an AC tach and a DC voltage for a brush type of tach.
And I am still bothered by the lack of any picture of the back, showing the connections, on that amazon link. What are they intentionally hiding?? And certainly it was not an accident that the back was not shown.

 

The ones that were common in my other post were brushed DC, they simply interacted with the analogue (DC) servo signal being applied.