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.
"Proper effort is not the effort to make something particular happen. It is the effort to be aware and awake each moment." - Ajahn Chah
"When we see beyond self, we no longer cling to happiness. When we stop clinging, we can begin to be happy." - Ajahn Chah
"Know and watch your heart. It’s pure but emotions come to colour it." — Ajahn Chah