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.
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The American Heritage® Idioms Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.