since you say these are from the '80s I might guess NOT varnish-set (generally quite earlier) or water-slide (next gen) but could be some variety of "rub-down" transfer, AKA chroma-tec (a trademark I probably misspelled, but it was sometimes used as 'generic').
If so these were made with a process that used hand-applied lacquer inks sort of akin to screen-printing yet different) on a release paper (or plastic film) and the final coat was the adhesive which could be a sticky wax or something more refined...but you might have adhesive coating that's dried up and will not stick. The way these are applied is you position them on your surface, sometimes helped to tape with a low-tack removable tape, then burnish over the transfer with a smooth tool made for this and CAREfully peel up the carrier paper/film as the transfer sticks to your surface...it often was nerve-wrackingly slow and dicey cause the delicate thin lac inks could crack and separate if you lost patience, and some of the adhesives did not like the surfaces you applied them on. If you DON'T have such 'chroma-tec' transfers then this is all a bunch of useless trivia...until you do!
Forgot to mention that the final steps were laying a clean paper over the transfer and burnishing over-all to fully smooth and stick flat, then if you wanted protection (the lac inks were surprisingly fade and weather resistant but really easy to scratch!) you could clear-coat them but this was a VERY risky deal. Since inks were lac-based any clear with acetone or MEK could "melt" them, and safe clears like Kristal Klear acrylic still had to be tested first just to be sure. If you had a safe one you went slow and misted a first couple coats and allowed drying before adding heavy coats to build.

DOH! re-read and you say these are "old water-slide" so ignore all written above, unless it turns out this is helpful after-all for somebody else or for the "next time"