The FTC would look at people who recently bought short term call options against Eli Lily stock and ask them questions. Pretty much the same playbook anytime bad news causes a stock price to go down. Matt Levine notes this as a common way people get caught doing insider trading each time it comes up.
It's normally combined with recorded IM conversations along the lines of "bro, I bought some short term chickens for Lli Eily. Let's make them CLUCK with this tweet." You call them chickens, or something similar, to try and fool the FTC. This is also a surprisingly common occurrence during insider trading investigations.
The SEC definitely targets sudden, surprising stock moves, and looks for people who profited off them. (This is why one of Matt Levine's tongue-in-cheek 'rules for insider trading- this is not legal advice!' is never do it in short dated, out-of-the-money options!) I'm sure there are relatively sophisticated ways to exploit the market that the SEC probably won't catch (that are also more sophisticated than I understand), but now you need to have a sophisticated understanding of the market, and of cybersecurity fraud (to beat Twitters payments verification), and naturally maintain flawless opsec on both throughout. Harder and harder to do.