Glue for Woodgrain Trim on Dash Bezel

[72malibu]

I pulled very nice woodgrain plastic trim off of a broken non-ac dash bezel and plan to install it on a new repro ac bezel with fresh chrome. This is for a '75 truck.

There was a lot of butt puckering when removing the woodgrain, but I managed to get it off without hurting it. Interestingly, the remaining glue on the woodgrain and the bezel (some stuck to each) is still tacky.

Does anybody know of a plastic glue that is strong and remains tacky? I'd like to use something similar to what was originally used. It's some sort of clear high-tack adhesive that doesn't fully dry out.