John P. wrote, among other things,

"The pattern of how this sinusoidal current varies in both phase and
magnitude is very different in the two cases (standing and traveling
waves), but you need both a phase reference and multiple locations to
see the differences. "

Do you really need the phase reference? Traditionally (since the
beginning of measuring them, and sometimes still today), standing waves
on a uniform transmission line have been measured by finding a point of
minimum amplitude (as measured by voltage, or alternatively by current)
and a point of maximum amplitude, with no reference to phase. In fact,
SWR was reasonably defined as the ratio of max/min amplitudes. If you
know that the wave you're observing is a sinusoid and you have min and
max amplitudes along the line, then you can resolve the wave into two
travelling-wave amplitudes; you won't know which is which but you will
know the two amplitudes. If there is but one source in the system,
it's reasonable to think that the higher amplitude travelling wave was
the one coming from the direction of that source.

In fact, you don't even need to find the minimum and the maximum
points. Again, given sinusoidal excitation and a uniform line, some
small set of points with accurate amplitude measurement at each will
suffice, since they will uniquely determine the amplitudes of the two
waves and the line attenuation. You would have to know the spacing of
the points and that they were dense enough that there is not a spacial
aliasing problem (points distributed over more than 1/4 wavelength...).

It's common to think of a standing wave as the result of two travelling
waves, one in each direction, but another way to think of a standing
wave pattern is as a pure standing wave plus a pure travelling wave.
The minimum-amplitude represents the amplitude of the travelling-wave
portion. The difference between max and min represents the amplitude
of the standing wave portion. For some folk, it's enlightening to see
an animation of the waves for several different values of SWR.

Cheers,
Tom