Is it the jack itself that’s wiggling, or the plug won’t stay in the socket and wiggles too much?

If it’s the latter, take a staple and bend it straight, and VERY GENTLY drag it round inside the port, avoiding contacts, scraping out the lint and dust that has almost certainly become impacted at the base of it over time. I do this whenever cables don’t want to stay in anymore and it’s amazing how much of a difference it makes.

I have had one example of the port itself becoming loose, but mostly I’ve run into the lint/dust problem.