Gene, W4SZ wrote:
"Your favorite example of an ideal transmission line with a perfectly
reflecting termination shows exactly the same thing."

Yes. Several readers have available Terman`s 1955 edition of "Electronic
and Radio Engineering". On page 94 is Fig. 4-5, "Phase Relations on a
Transmission Line for Two Typical Conditions".

One of the conditions is for a complete reflection (Rho = 1). The phase
changes are indeed abrupt. Over a distance of 1.25-wavelengths we have 5
abrupt transistions of power factor between 90-degrees lag and
90-degrees lead or vice versa. The similarity between a standing-wave
antenna and a standing-wave transmission line would lead one to expect
abrupt phase reversals on the antenna too, as the open circuit at the
antenna end is an abrupt almost complete reflection maker.

Best regards, Richard Harrison, KB5WZI