Transformer mains identification
I've since found that some of the APC series UPS units have these transformers as part of active circuitry in order to trim/boost output voltage.  It all seems to simple now...







simulate this circuit &ndash; Schematic created using CircuitLab

"Normal" is the state in the diagram, we see that the AC only goes through XFMR1.

"Trim" is when SW1 is thrown, since then the AC flows backwards through XFMR2, subtracting from the XFMR1 output.

"Boost" is when SW2 is thrown, since then the AC flows forwards through XFMR2, adding to the XFMR1 output.

Mystery solved.