Social media platforms offer users multiple ways to engage with content--likes, retweets, and comments--creating a complex signaling system within the attention economy. While previous research has examined factors driving overall engagement, less is known about why certain tweets receive unexpectedly high levels of one type of engagement relative to others. Drawing on Signaling Theory and Attention Economy Theory, we investigate these unexpected engagement patterns on Twitter (now known as "X"), developing an "unexpectedness quotient" to quantify deviations from predicted engagement levels. Our analysis of over 600,000 tweets reveals distinct patterns in how content characteristics influence unexpected engagement. News, politics, and business tweets receive more retweets and comments than expected, suggesting users prioritize sharing and discussing informational content. In contrast, games and sports-related topics garner unexpected likes and comments, indicating higher emotional investment in these domains. The relationship between content attributes and engagement types follows clear patterns: subjective tweets attract more likes while objective tweets receive more retweets, and longer, complex tweets with URLs unexpectedly receive more retweets. These findings demonstrate how users employ different engagement types as signals of varying strength based on content characteristics, and how certain content types more effectively compete for attention in the social media ecosystem. Our results offer valuable insights for content creators optimizing engagement strategies, platform designers facilitating meaningful interactions, and researchers studying online social behavior.