The act of sneakily watching someone else's screen, typically without their knowledge. This can include peeping at a phone, tablet, or computer screen to see what they're watching or reading. Often done out of curiosity or boredom, especially when one's own device is unavailable or uninteresting.
Example 1: My phone died on the subway so I was eaveswatching TikToks from someone's phone who forgot headphones.
Example 2: I was watching Friends on my phone and heard my girlfriend laughing along, which means she is as Eaveswatching when you texted me.