I am going to suggest taking it to a frame shop and having them put it on a lift, hang the gauges and get the tram gauges out.
I bought this truck a couple years ago and looked over it carefully before I paid him. I knew it was wrecked at some point because the left 3/4 front sheetmetal was replacement GM parts with stickers. Crawled underneath it, didn't see anything that was a deal breaker. It drove ok after changing a couple bad front end parts and new tires, had the transmission rebuilt, they didn't say anything.
Pulled the bed and dropped both tanks and found the frame kinked in the center, the tanks blocked the view. When they "fixed it", they bent the cab mounts to level the cab. I had previously ran a Carfax prior to purchase and there was no accidents listed and it was one previous owner. I bought it off the grandson of the 90 year old couple going into assisted living home.
First, found a guy who could do it, not easy today with production shops everyplace here, he racked it and showed me 5 other areas out of place. I have been waiting for him to get to it, he is 4 months out on appointments.
With these trucks being around 35 years old, many of them have numerous stories hidden in them. With this being wrecked in the front and a loaded trailer swinging off the hitch at the time, I can only imagine what they will find.
The shimmy that comes and goes, I would bet is a tire with a shifted belt. Quick test is to lower the air pressures in the suspect wheel and take it for a spin. I used to shift belts all the time running at max PSI on company trucks, drop them dow so it drove better and the shifted belt went away.
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