Do you listen to your music with your eyes open or closed or a combination of both?

Both, but I prefer to keep them open while the room is as dark as I can get it. I also always remove my glasses @immatthewj I think I read about this little tweak in Listener years ago and it definitely makes a difference, at least for me. It certainly stands to reason - you are basically removing a highly reflective surface from a spot inches in front of your ears.

I listen exclusively at night, blacked out room, I do combo, mostly closed however. I want no distractions during my listening sessions, no visual stimulation for me.

Well, both, but if I keep my eyes closed for too long I fall asleep !

Both - it often depends on the music.... 

@sfgak 

I am an amateur musician, and when I play guitar, it is often with my eyes closed. I find that I can “visualize“ the fretboard better with my fingers than with my eyes.

I wish I'd gotten into that playing habit, but after 50 years, that's a big ask. Looking at the fingerboard is definitely not good for my neck so I'm currently experimenting with postural changes to see if I can lessen the negative impacts. 

I find when listening to live music, I often close my eyes. Not so much, when listening at home.  I can only conclude there are typically more distractions in a live venue.