one eye on
one eye on (someone or something)
Partial or intermittent attention given to someone or something. She shoveled fuel into the boiler with one eye on the pressure gauge. You cannot just keep one eye on the kids. The moment you're not paying attention is all it takes for one of them to get hurt.
Farlex Dictionary of Idioms. © 2022 Farlex, Inc, all rights reserved.
*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.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
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.
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.