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What kind of oil? Thought it might be lithium grease or something similar?
This may not be the best choice, but it was definitely the cheapest. I just squirted some WD-40 into the setbelt swivel. Used the little red WD-40 pipe to give it just the smallest squirt. Then worked the swivel back and forth a bit and the squeek has been gone for 6 months.
My theory is that the swivel just got some dust or dirt in it and the WD floated it out of the contact area.