Cecil, W5DXP wrote:
"How is it possible to use a signal (standing wave current) that is
known not to change phase, to measure the phase delay through a wire or
coil?"

Ignore it.

Lissajous figures result from applying signals to the vertical and
horizontal deflection circuits of an oscilloscope simultaneously. Phase
difference between signals of the same frequency make a distinctive
pattern.

One can use coax lines with identical delays to couple the inputs with
phase sampling loops. Take samples of the currents at the two points
where the phase difference would be known. Amplitudes can be adjusted
for a suitable pattern. It will be destinctive.

Then take samples from the same source. Add a known delay to one channel
until you have reproduced the distinctive pattern you had observed when
testing the felay between the points that have the unknown phase
difference.

With a few elaborations, that`s how a phase monitor works.

Best regards, Richard Harrison, KB5WZI