trace vs keep an eye on

trace is a noun but keep an eye on is not a noun.

Word	Noun	Adjective	Verb	Adverb
trace	Yes	No	Yes	No
keep an eye on	No	No	Yes	No

trace (noun)	keep an eye on (noun)
a drawing created by superimposing a semitransparent sheet of paper on the original image and copying on it the lines of the original image
either of two lines that connect a horse's harness to a wagon or other vehicle or to a whiffletree
an indication that something has been present
a suggestion of some quality
a visible mark (as a footprint) left by the passage of person or animal or vehicle
a just detectable amount

trace (verb)	keep an eye on (verb)
follow, discover, or ascertain the course of development of something	follow with the eyes or the mind
read with difficulty
make a mark or lines on a surface
copy by following the lines of the original drawing on a transparent sheet placed upon it; make a tracing of
pursue or chase relentlessly
to go back over again
make one's course or travel along a path; travel or pass over, around, or along
discover traces of