to watch a streaming TV series, either several episodes or a complete season, usually in one sitting
He missed Breaking Bad when it was first on, and now he likes it so much that he's eye guzzling all of season 1
An extended gawk or to binge watch a TV series or movie serquals.
1) Jim was eye guzzling that co-ed so hard I thought his eyes were going to fall out.
2) I spent the entire long weekend eye guzzling the last 3 seasons of Game of Thrones. Now I'm in a massive show hole.