Roy Lewallen, W7EL wrote:
"Certainly, the total V and I are in quadrature if the line is
terminated by an open, short, or purely reactive load. But not in any
other case."

Something else is at work. The reflection reverses direction of the wave
producing a 180-degree phase shift in either voltage or current, but not
both, if there is a reflection. Because the waves are traveling at the
sane speed in approaching each other, they produce a phase reversal in a
distance of only 90-degrees instead of 180-degrees. This places the
waves in quadrature to stay. Terman shows the vector diagrams of
incident and reflected waves combined to produce a voltage distribution
on an almost lossless transmission line (Zo=R) for an open circuit case
and for a resistive load case where the load is Zo in Fig. 4-3 on
page 91 of his 1955 opus. Indeed, the angle between the incident and
reflected voltages is 90-degrees in either case.

In Fig. 4-4 on page 92, Terman shows voltage and current distributions
produced on low-loss transmission lines by different load impedances and
in every case volts and amps are in quadrature.

Best regards, Richard Harrison, KB5WZI