Brake cleaner? Better wipe that off in a hurry, Bronc. That type of solvent can be absorbed into soft plastic and cause swelling. See can to confirm whether your specific chosen product is OK on car paint. To remove old tape, soften with solvent or lubricate with soapy water or glass cleaner and carefully scrape with a plastic instrument, maybe a used-up gift card or something like that. So you don't damage the paint. Solvents exist that can be used on modern clearcoat paint. Such as wax and grease or bug and tar remover, goo-gone, adhesive remover, nail polish remover, etc. But around the house I use WD40 while I scrape old tape. It stays wet for a spell, so you can scrape. Special "eraser wheel" or "hockey puck" tools are available for those who do it a lot. They work like a pencil eraser. Often a guy can slowly peel up the old tape with fingers if it is still in decent shape.
Once the surfaces are free from tape, they can be cleaned. Wash first with soapy water (or squirt glass cleaner down in there, if the molding is still partially attached) and paper towel it as best you can then let it air out so at least your tape area is dry. Now you're ready for alcohol, to final clean. Isopropyl alcohol is cheap and at stores of all kinds and in varying strength. The place where you got that tape probably has some sort of packaged alcohol prep wipes just for this if you don't want a whole bottle.
You'll be OK if its over 60 degrees, the 3M tape stays soft and sticks well. Heat makes it softer. Never a bad idea to keep an eye on a molding like that for a couple days in case it needs more pressing down though. They almost all (3M) have red backing (sometimes I see green liner on black tape) but you might have black, grey, or white foam tape in the package. They would all work. Just mash hell out of it when you stick it, and go over it a couple times just don't make a dent lol. If you do these things, you'll give it a sportin chance at staying put.