Refers to doing another activity with less focus while primarily engaged in something else. He had one eye on the report while watching the football game.
Pro Tip 2/3
Distraction Awareness
Suggests awareness of potential distractions that could interfere with the main task. While studying, she kept half an eye on her notifications.
Pro Tip 3/3
Alertness
Implies readiness to respond quickly to a change or need while engaged elsewhere. I have one eye on the weather in case it turns bad during our hike.