1kHz is just the frequency of the tone - it's a common frequency for a test tone. The level you feed to the unit, rather than the frequency, will affect how you interpret subsequent VAC readings in the circuit. A good reference point is 0.775VAC = 0dBu, and 1.228VAC = +4dBu = 0VU (in many typical studio applications, although 0VU is not a true standard value but a reference level). This will not always have a consistent relationship to dBfs levels displayed within a DAW, but I seem to recall that the last time I was calibrating something a tone generator plugin set at roughly -18dBfs gave me 0dBu on my interface's analog output - I could be misremembering though. You can measure AC voltage between pins 2 & 3 on the XLR input to see what you're actually feeding the unit and adjust it accordingly. Maybe try starting with a 0dBu/0.775VAC signal.
I would say that 0.003VAC is effectively 0VAC, for all intents and purposes. So with the unit engaged, I would think having that on pins R and T might indicate a problem. That would mean that, assuming your reading of the schematic is right, no signal is reaching the 10468 transformer. (Sorry I am not double checking the pin out as I write this, I am on my phone and it's a little clunky to try to look through schematics on here).