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Good luck. I tried two different sets of letters and could not get them to stick. I cleaned the dash with iso alcohol, denatured alcohol, and also 3M Adhesive Cleaner hat cleaned the 2 sided sticky tape of body side molding. I finally gave up.
You could try contacting southern car parts and see if they have any of the cyberdine graphics raised letters in stock because they stick very well and you just need to clean the dash with soap and water - install link. There is another vendor on here who had some as well but i forget who.
Those flat decals will probably never go in right and stay in. Get 3D raised letters. They look great and stay put.
I got a set of the decals first and it came with two sets and a note that if they still don't stay in they would sell me more decals at half price. Not a good sign they stay in. and they didn't. Have had the 3D ones for months and they are great. and look better raised than the flat decals.
3M spray adhesive , spray a dab onto cardboard and use a small brush to tack a small amount of adhesive onto the back of the lettering.Too much cleaning with alcohol can brake down the bonding surface . Luckily the alcohol didn't eat up your whole dash or make it turn white. I NEVER use alcohol for cleaning, ONLY for cuts and scape's and that's it. I would clean the alcohol dash surface well before trying again simple clean water and some mild soap and let dry well, should have you prepared enough to bond well.. IMO. Mine stuck like chuck the first time, with no do overs..
Wish I could help. I deal with vinyl everyday. I have a full digital graphics shop, but I'm not sure what you're trying to do (what type vinyl, where is it going). I do know newer dashes are made so that stuff doesn't stick them. There's something in the ABS plastic. I tried wrapping my dash parts with printed Burl Wood and it stuck great for a few days then started curling up. I know I did everything right, I've been in this for 20 years & suppliers use me as an info port for their new clients.
Get some q-tips,and clean out the indentations on the dash 3 or 4 times with acetone-don't get carried away and let it run down the dash-it may leave streaks.
When it dries(which is really fast) take a sliver of scotch tape and see if it sticks-if it does,you're set,if not,clean them out a few more times.
If your car is older like mine,there may be years of armor-all,or some other slippery crap to clean out of the letters,so it may take awhile to get it all out-but when you do,they'll stick fine.