I was told an article on heise.de said finding flight data for Elon Musk's plane was actually not very easy, so I got bored and tried to find it with zero info from @elonjet, @JxckS, /r/ElonJetTracker or similar, and it was actually surprisingly easy, even for someone who doesn't know a lot about aviation.
A search for "Elon Musk private jet" on DuckDuckGo gave me an article from Firstpost about Elon's Gulfstream G700, which mentioned his plane being registered to "Falcon Landings LLC"
Searching for that LLC and "registered planes" gave me a few results, one from Jack Sweeney which I ignored to play by my rules, and one from aircraft-data.com, which listed a single plane, a Gulfstream G650 with tail number #N628TS.
Looking up that tail number on FlightAware gives me a funny message about the plane's owner requesting that data to be private, but I found another site called https://globe.adsbexchange.com, ran by aviation enthusiasts and who refuses to censor any data of any plane, where you can filter every known plane in flight by tail number on a list.
His plane isn't airborne right now, but it's funny that I was able to find how to track it with barely any prior knowledge in about 5 minutes, way less than what it took me to write this post. "My plane is actually not trackable without using non-public data", my ass.