91 K1500 pulling after tire rotation?

I did an oil change the other weekend, and thought while I was at it I would do a tire rotation. After the tire rotation, the truck had a horrible pull
to the right. My tire shop told me the tire was at fault, and to rotate it to the back....something about how the belts settled, etc.
So I rotated to the back, and the pull went away, /almost/ It now has a gentle pull to the left!! WTF is going on here? Obviously to get the best tire wear, I need to rotate often. But how can I if specific tires cause the truck to pull?????
This pull is a "let go of the steering wheel, and see what happens test". Tried it on all sorts of straight, smooth roads, same results. What else might cause a gentle left pull? I don't have to fight it with the wheel, and there doesn't seem to be any noticeable indication on the front tires of a failing front end part? thoughts?

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