I forgot who got me started on that but closing my eyes and listening once I am "settled in" on a mix is part of my process.
Part of my process is similar. Although i usually don't close my eyes. But i tend to stare at one point on the console basically ignoring my eyes. Then i 'inventory' the band and make sure i can hear everything clearly and distinctly. I find if i do it while looking at the band my mind fills in the missing sound using the visual cues i'm seeing. Eliminating those cues gets me a better/more accurate result.
Once i've dialed in that fairly balanced mix of course i actually do pay attention to the stage so i can see changes and solos, etc. But my first step is the Zen of the Stare....