Goof-Off is very caustic, and will readily damage many plastics and paint. However, it is an object lesson in salvation
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Goo Gone is a completely different product, and I've never had any problems with it. Great for removing price stickers, etc., from just about any surface. It's the first thing I reach for before taking more drastic measures.
I've never tried it with gum, but I'm confident that at least it wouldn't cause any damage in your engine compartment.
Here's a handy "idiot proof" shopping list: