I'd avoid anything too thin, like ATF, Marvel Mystery Oil, even 3 in 1
I use a mixture, the main ingredient is Bars Rear Main Seal Repair oil.
But I wouldn't say go out and buy a quart of it to fillup (2) dampers that only hold 3.5 cc's. But if you can find a use for one of the oils that are advertised as being for high mileage engines, I'd get that.
The reason is that both those oils keep that little PIA to replace O-ring around the needle adjuster plump and leak free.
I put some Bars in a leaking carb 4 years ago and still holding.