If your antenna is a slotted waveguide array, the antenna pattern (pointing direction) depends on the amplitudes and phases at each element, just stating standard array theory.
If you place a mismatch at the input to the antenna that's far away from the antenna (i.e. your flex guide), and vary its' VSWR with pressure, then the energy getting into the slots of the antenna will change due to that remote reflection. This standing wave will change the amplitude and phase energy arriving at each of your slots in the antenna and hence the antenna pattern pointing direction will change with frequency. If the mismatch is really close to the antenna, maybe things won't change as much with frequency, but having it further away changes in-phase reflections to out of phase reflections quickly.
Pressure changes could be changing the effective dielectric constant in the waveguide or the size of the waveguide (rf travels faster with a larger waveguide size, a pseudo-lowering of the dielectric constant of the air in the guide). That would shift the VSWR mixing from the source to the antenna also, producing antenna pattern shifts.
As an example;
if you were an engineer in 1965 and using a slotted waveguide VSWR measurement device on your antenna, say the antenna was 2.5:1 VSWR, and then you added a mismatch on the input side of your slotted waveguide, you'd see the Voltage Standing Wave shift, both in amplitude and phase. Pretend the location you move the probe back and forth is now the elements radiating from your antenna (a serial slotted array antenna). The amplitude and phase changes all along the radiating elements which changes the antenna pattern. Most antenna pattern shapes don't change when the VSWR of the input cable/waveguide changes, but the slotted waveguide array is different since it's a traveling wave antenna.
Or so I think.
I haven't researched this, just paused and thought about it. Feedback would be appreciated.
You could try an experiment, try squeezing or moving your waveguide a bit to see if you can detect antenna pattern shifts. Have you heard of the old trick of the strong magnet and metal ball inside the waveguide for dent tuning of waveguide. That might demonstrate things.
kch