To OP
this is a long shot but...
I noticed on the Trane wiring diagram that you posted that the
connections for the IGNITION circuit are shown to be near to the
connections for the primary of the transformer.

If there is some insulation problem on the ignition wires and the VERY
high voltage from the ignition circuit is sparking or jumping over to
the transformer primary circuit, this could cause the symptoms you are
seeing.

Make sure the wires that are part of the ignition circuit are not even
close to the anything else. and inspect them (with the power off) for
any sigh of cracks or other faults. These have very high voltage
like in a car spark plug and can jump several inches if there is an
insulation problem. And the problem would be intermittent. The
transformer primary voltage would look perfect except when the high
voltage spark jumps over to it and this could easily damage the
insulation on the transformer which is not designed for very high
voltages.

If you are an electrical novice, you may want to think about calling
in for some help at this point.

Mark