I have PN on rh side only but both piriformis muscles are painful, although right more so. piriformis stretches on rh side are more painful too. However if I do too much, both muscles then increase in pain jointly and involve hips then groin in that order. Doubt that helps you much but one thing that may be relevant. . . .my r side sacroiliac joint has no 'spring'. . .have you had your SI joint assessed like this? it is an easy test although someone else needs to do it. Just lie on your back and have someone, physiotherapist or whomever put their hands on your hip bone and press down slightly a couple of times, no great pressure is required for this. . . . please be cautious if tried.
I have had someone press down on my SI joint from above, thru' a bent, raised leg. . . . nothing, no pain at all (although not the same as the method you describe, possibly similar 'mechanics'??) But this other 'spring' test showed that the right side was stuck while the left side is normal and springy. I can feel the difference when this is done too.
I have had about 6 different physios try and fix this imbalance but if it ever worked (I felt no better but they said I was fixed) it certainly didn't
stay fixed as the next physiotherapist said my pelvis is up and rotated and 'fixed' me all over again. I began to think that this was physio speak for 'give me your money' and I have given up getting 'fixed'
Piriforms syndrome is fairly easy to detect, have they worked on this muscle at all? Painful?
Did all of these symptoms come together?
If the PN pain was noticeable on that one side first, it may be that you hold yourself slightly differently because of pain and this compensation has lead to piriformis syndrome on the opposite side?? So yes, nerve driven but not directly? Just a guess but try that 'spring' test if you haven't already.
if you are less 'free' on one side then the piriformis muscle may need to compensate too, causing it to tighten. Have you tried easy piriformis stretches? They can work like magic but it will depend on how tight any muscle has become. Myofascial release and acupuncture can help too, acupuncture straight into the muscle itself OR if too painful (was for me ) around the periphery.
None of this has worked for me because the piriformis is the cause of my problems due to a lump/haematoma that formed there after a fall, resulting in scar tissue compressing/entrapping the nerves. Most people have piriformis syndrome
because of PN so good targeted treatment can work

a treat, although as this muscle is deepish it tends to mean a LOT of butt rubbing
Take care,
Helen