english
1
general::
Phrase(s): *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.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
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.
American Heritage Idioms