I've had fairly good luck with WD-40.

The problem with packaging tape is the adhesive is designed to be permanent, unlike painters tape which is designed to be removed. Most adhesive removers will damage your door because they are xylene-based. You might try to find 3M citrus based adhesive remover. You might try soaking paper towel with vinegar and laying it over the stains. Whatever you try, you need to let it sit on the adhesive for about 10 minutes, then scrape with a plastic scraper. Good luck (and never use packaging tape ever again if you want to remove it later)

Tried the WD-40. Unfortunately, no success.

I have tried to warm up left-behind adhesive with a hair dryer and scrape. Sometimes it works, mostly it doesn't.

Sometimes extreme cold applied to adhesive will cause it it harden and scrape away better.

The best luck I have had is to let the stuff age for a year or so and then scrape it.

As a female, I have a different suggestion: How about trying nail polish remover? The "acetone" kind is stronger. Available at drug and beauty supply stores. Good luck!

Hopefully the goof off didn't damage the vinyl. Be careful with that product and the nail polish remover.

Have you tried Dawn dish detergent? Put it on full strength and possibly cover it with syran wrap to keep it moist. Let it set and use something to gently scrape the glue. Maybe even try a kitchen scrubby sponge that you use for nonstick pans. Also another thing would be a product call Oil Eaters. You would find that at an auto supply store. It works well to help remove wet paint from brushes and black marks that run down the side of rv's. I use it for removing a variety of problems.

DO NOT, under any circumstances, use nail polish remover on a plastic door, unless you want to ruin it. It is acetone, which dissolves plastic. It may remove the adhesive, but part of your door will be removed as well.

Eucalyptus oil is commonly used here.

They make a goof off especially for plastic, I'd try that. It's purpose is to remove adhesive from plastic so I can't see why it wouldn't work in duct tape adhesive.

I took a label off a plastic pill bottle and it left a sticky mess on it.

I rubbed the mess off with 99% rubbing alcohol first, then with the remaining residue rubbed it off with baby oil. Then just wipe off the baby oil. The bottle came out just like new and never left any marks on the plastic at all.

I just used a small makeup remover pad to apply the solutions to.

Try butane. Test it first. I watched a woman at a gift shop wipe price sticker adhesive off an expensive piece of porcelain with it. Since then I've used it to get a lot of adhesive of a lot of surfaces, including ancient scotch tape off 120 year old silver. I squirt the butane on folded paper towels and wipe. It might take a little elbow grease, but after a few wipes it generally starts to lift right off.