It's much more common to meditate with your eyes closed, though eyes open can be a good antidote for sleepiness.
The trouble with the eyes half open idea is that it takes a bit of attention to maintain the eyelids just right, attention that would probably be better put on the meditation object.
"Right effort is effort with wisdom. Because where there is wisdom, there is interest. The desire to know something is wisdom at work. Being mindful is not difficult. But it’s difficult to be continuously aware. For that you need right effort. But it does not require a great deal of energy. It’s relaxed perseverance in reminding yourself to be aware. When you are aware, wisdom unfolds naturally, and there is still more interest." - Sayadaw U Tejaniya