Any Les Paul with the same pickups as the one you like is a good place to start. But there are too many variables between guitars to ever find a “sound alike” for one you like based on specs or year of manufacture.
Pristine Gibson Les Paul Custom in Cherry Sunburst with W/B/W/B/W double sided binding. The white has turned to a cream color This guitar is labeled as a second from the factory due to a finish flaw. If you look closely at the Gibson on the headstock you will notice the there is a slight rid...
(sorry just having some fun ) for real though, having owned my fair share of les pauls from all brands including Gibson, having previously and currently own multiple of the same guitar year, manufacturer, and model each had its own personality. a few were close but none exactly the same.
I had a lovely Tokai Love Rock from around that time that I convinced myself sounded just like a Les Paul Standard. Had it for years and loved it, but in reality it sounded like itself. Brilliant guitar, but not the same pickups or hardware and not a soundalike. And not cheap from memory - circa half the price of the Gibson though i may have that completely wrong. No idea about availability or prices these days but might be worth a look?
Why 1986? Is it a specific instrument you are trying to mimic? I certainly can't date a guitar by just listening to it for example. And any pedals in the chain will also change the tone of course. Sounds to me like you need to spend a happy few days trying out guitars then buy the one you like the most. Good luck and remember to post some pics once you have it.