Given that, from Find Familiar:
A familiar can't attack, but it can take other actions as normal.
Eye Rays. The gazer shoots two of the following magical eye rays at random (reroll duplicates), choosing one or two targets it can see within 60 feet of it:
The rays aren't listed as attacks, so I lean on "yes, it can". On the other hand, it seems much more powerful than other familiar forms.
I am not sure if the Gazer Variant found in Volo's Guide to Monsters (page 126) behaves the same as the familiar Gazer in Waterdeep: Dragon Heist (page 105). If there are differences between them, an ideal answer would cover that as well.