have half an eye on (someone or something)
To watch someone or something intermittently or half-heartedly while something else is happening. Unfortunately, I don't remember what that list said because I had half an eye on the TV while Mom was trying to show it to me.
have one eye on (someone or something)
To watch someone or something intermittently or half-heartedly while something else is happening. Unfortunately, I don't remember what that list said because I had one eye on the TV while Mom was trying to show it to me.