ProForm Products has two types of cleaners that I use. One is a very strong PF621 Wax and Grease Remover. If you use too much of it or leave it on painted surfaces, you will see paint on whatever you use to wipe it.
The more gentle one that I use for preparing and cleaning just about everything is PF620, Final Wipe. It's what you're suppose to use prior to painting, in between primer and paint coats to remove tacked on dust, and can even be used on painted surfaces after they've been cured for a day or so without harming them much if at all. It works well on vinyl if you get a bit of contact cement or spray glue build up and doesn't seem to damage the vinyl used in this reproduction kit. Infact, if there are any areas where you needed to use heat on the vinyl that slightly glossed over, you can use the final wipe and it seems to normalize the contrast between shiny and dull areas, but it doesn't seem to dull the area that are already like that.
I really like it.
For the old glue, just wet a cloth with the PF621 and dab some on the glue, then use a dollar store tooth brush (for some reason the 2 pack of toothbrushes with the rubberized grip from the dollar store don't melt in the solvent like the full acetate ones do) and work in circles to move the glue around. The glue will just clump up and ball up on the tooth brush. Wipe it off the toothbrush to prevent further smearing the glue around the rest of the piece, and continue.
It didn't seem to harm the rubber backing on the side-sill material, and actually made it a bit more rubbery. I'm sure if I left a big puddle on there, it would do some damage, but cleaning it with dish soap afterwards makes it nice.