with one eye on
with one eye on (something)
While giving something one's intermittent or partial attention. I hurried to finish the report with one eye on the clock. She shoveled fuel into the boiler with one eye on the pressure gauge.
with one eye ongiving some but not all your attention to.
1977 Craig Thomas Firefox With one eye on the JPT (jet-pipe temperature) gauge he opened the throttles until the rpm gauges were at fifty-five percent and the whine had increased comfortably.