one eye on

*one eye on someone or something

Fig. [get/have] a small amount of attention devoted to someone or something. (*Typically: keep ~; have ~.) I have to have one eye on you at all times or you will get into trouble. I have one eye on the speedometer of my car whenever I am driving.
See also: eye, on, one

one eye on

Paying some but not full attention to, as in He ran the rehearsal with one eye on the clock. Also see have one's eye on; out of the corner of one's eye; see with half an eye.
See also: eye, on, one
References in classic literature ?
When I returned with the rum, they were already seated on either side of the captain's breakfast-table--Black Dog next to the door and sitting sideways so as to have one eye on his old shipmate and one, as I thought, on his retreat.
This night she hurried to bed purposefully, every hair up, one eye on the stranger, who had dropped on a mat in a helpless, hopeless sort of way, all four feet spread out, sighing heavily.