I would use a hair blower to remove the badges. Then use goo-gone, or other no alcohol based remover, with a paper towel/rag to remove the adhesive. Worked great on my 04 and didn't damage the paint.
The letters look like they're held on with a plastic retainer...while the "GT" badges seem to be a nut.the emblems on a 66 are not glued on! first you have to be able to reach the backside of the emblem. most have a push on clip that will explode when you pull it off, others have speed nuts. take your time and be careful, metal badges and letters will ruin a nice paint job if you are not careful. :bigthumbsup