Can T. rex see you if you don't move?
Yes, it could. Standing still would not hide you: that idea comes from a film, not from its eyes. By the reconstruction from fossil skulls, T. rex saw about 1.4 times more detail than you, so it could spot a person standing still from further away than you could.
Stand still and test it
At 100 m you can make out a person standing still. T. rex (reconstruction) could make out the same person from about 140 m.
Bigger means clearer: a sharper eye sees you in as much detail as a person standing closer would. Standing still changes nothing.
A simulation made from published eye studies. Not what the animal feels.
Face-off: Tyrannosaurus rex vs allosaurus.
Can T. rex see you if you don't move?
Yes. By the reconstruction, its eyes picked up about 1.4 times more detail than yours, and nothing about an eye stops it seeing something that keeps still. The "don't move" rule is a film idea.
How well could T. rex see?
By the reconstruction, about 1.4 times more detail than you. The zone both its eyes saw together was about half as wide as yours (reconstruction), so it judged distance with a narrower front view than you.
How do we know what T. rex saw?
Nobody can test a dinosaur's eyes. Its eye size comes from fossil skulls, and its sharpness comes from how eye size and sharpness go together in living relatives such as birds. So treat every T. rex number here as a reconstruction: a best guess.