I know from research and combing through threads that it does vary. A few years ago they came out in March. However, the lab you applied to makes a decision and notifies AEEE of the decision, but then AEEE has to wait for all labs to turn in their decisions. So come late January, if you reach out to the lab (I hear) you may receive a response from them informing you of whether or not you made it.
You could look into NASA’s student internships? They have internships that are specifically for high school students, and combined high school-college ones. I’d also poke around the high school summer programs different colleges/universities have.
In addition to SEAP and NASA, I applied NSLI-Y (a language study abroad program which is a Department of State initiative), and they have interviews (the stage between semifinals and finals where only top applicants get one) on a rolling basis from January to March, so I’ll be refreshing my email seeing if I made either all the time then! NASA’s summer applications are also due in March, though decisions begin before the deadline so be sure to apply early!