Sodium benzoate the correct amount

is it solely by virtue of its acidic content?

Yes, not a lot of biochemistry is happy living at pH 2 - and the stuff that can live there is already happily living in your gut with a ph of 1

is there a kind of ratio (or other metric) of vinegar to know whether something needs to be refrigerated to keep from spoiling?

You mean foods already packaged in vinegar? It would depend on how well they had been cooked/sterilized before packaging and how strong the vinegar is. Industrially made pickles will be a lot cleaner than something you pickle at home, but store bought pickles are likely to use much cheaper, more dilute vinegar than your grandmother did.

what components can act to counteract vinegar's ability to preserve food?

Anything too alkali will neutralise the vinegar's acidity

can vinegar stabilize anything that otherwise would spoil?

Not necessarily, it has to be something where the vinegar can penetrate into the food - it's not going to preserve steaks as well as vegetables. And of course the vinegar taste is going to help if you are trying to preserve say strawberries! Also fungal spores can probably survive dormant in vinegar (if not grow) - fungal spores can survive dormant pretty much anything.

I haven't seen a butterscotch canned recipe but the ball blue book has a couple syrup canning recipes that look fantastic. If you do any canning you should have this book. The recipes are invaluable.

These recipes use the hot water bath technique. The extremely high sugar content would be enough to keep it preserved. Modifying one to be butterscotch should be straight forward.

I wouldn't try any experiments that reduce the sugar content because then we're getting into the risk-of-horrible-paralyzing-death area of canning.