Having a fairly excessive lumbar curve (and thus tight hamstrings) seems to create a disposition for SI problems, at least in my experiance.
A common cause of what you refer to as "buttwink" would definitly be tight hamstrings, most try to compinsate my focring themselves down which results in bad form. The most logical way to prevent or remedy this would be dynamic warm-ups pre training and mobility/static stretching afterwards.
I conquored it. But one day I rolled my ankle 3 times in 2 hours, which damaged some ligament in my ankle. The problem induced was a smaller ROM in my ankle before i feel acute pain. I cannot get my knees as far forward anymore so now I have taken a step back
I am going to an ankle specialist soon, so I will see if I can get my ROM back.
then move to a tennis ball against the wall, on the glute, glute medius, piniformis etc. Then to a hard ball on the floor later on
fixed me up good, I used to butt wink a little But I also did release work for my whole body. LOok at working on the obliques and spinal erectors as well, all the way up the back, plus bottom of the feet and calves. The fascia connects the whole chain up the backside of the body. If it's tight something will cause you sag
and yeah low bar position fullsquats, seem to be easier in keeping a tight arched lower back with zero butt wink for me I don't seem to lean over that much more either, in oly shoes
For me it was tight hammies, without a doubt. This makes sense, too, if you read Starting Strength, since the hammies anchor the pelvis. If the hammies are too tight, the pelvis will be pulled closer to the knee, which causes the back to round. To keep the pelvis farther back, the hammies must stretch.
Incidentally, this also increases power out of the bottom, since the amount of force a muscle can generate is directly proportional to the amount of stretch it undergoes during the eccentric. No stretch = no power.
Other things that helped were using a lower bar position and olympic weightlifting shoes, also espoused in SS. I do declare that if you squat like this consistently and are patient, you'll be a speed/vert freak. I know CoolColJ agrees.
Assuming you have good flexibility, focus on looking ahead in the squat while keeping the chin neutral, pulling down on the bar to keep the arch, and driving through your heels when you come up. High bar or low bar, this stuff applies.
And go as deep as your flexibility allows, be it below parallel or atg!!!