I keep my eye patch looped over the eye piece of the scope and hold it in place with the eyepiece cover at all times, it's that integral to my scoping efforts. I keep a back-up in my backpack because they cost $3.00 at most drug stores, weigh nothing, and so contribute to preventing eye fatigue! I will switch between eyes periodically to keep them fresh, and of course relax on the 10x binos when appropriate. No eye patch will ruin a whole glassing session for me, so yeah, I think you should try one out. May just solve your eye fatigue, or at least dramatically decrease it. Plus, who among us didn't want to be a pirate at some point?
Squinting is lame!