Can a doctor tell if there is a brain tumor by looking into your eyes with that light?

First step: The ophthalmoscope can identify pushing forward of the optic nerve into the eyeball, suggesting (among other possibilities) a mass lesion within the skull.

Possibly: The doctor cannot tell for sure there's a brain tumor just by looking in the patient's eyes. There may be a suspicion of a brain tumor based on the findings but not the final diagnosis.