Electronic – this transformer-like component with only two leads

The board designators seem to be following IEEE STD 315 (kind of).

CR or D: Crystal rectifier (Diode) T: Transformer.

My guess is that this is a common mode choke on the power supply lines.

This transformer thing looks like basically a tapped inductor.

Perhaps you can determine the inductance and turns ratio by applying a pulse signal through a resistor and monitoring the rate of rise of current through the resistor. With a fixed voltage, the current (and thus the voltage across the series resistor) should rise linearly with time (ignoring the coil resistance and the voltage across the inductor- so only for small voltages wrt the pulse voltage). In other words, if you apply (say) 5V through a resistor and look at the slope of the voltage across the resistor while it is still close to 5V.. the rate of change will be dv/dt ~= V/L, so L ~= V/(dv/dt).

The turns ratio is the ratio of the square roots of the inductances, measured with the other coil open.

There are other things that are important in a flyback converter- especially the saturation current, but this should get you started. Probably the core is gapped (an air gap inserted in the magnetic circuit) to keep the core from saturating. It will be difficult to determine the number of turns non-destructively.