Are you susceptible to a creatures Gaze attack when viewing it through Arcane Eye?

I was in a game a while back, where my party and I were checking out a location where we are 80% sure a medusa was residing. Lots of stone statues around, missing people reports, etc. I had the idea of scouting the location out from a distance using Arcane Eye, to get an idea of the layout. About halfway through checking out the place, my brain kicks the idea: "Can you get turned to stone though the Arcane Eye?" At that point, I decided better safe than sorry, and dismissed the spell. I asked my DM afterwards, but he just said "Well, maybe you would have been fine maybe not" and wouldn’t give me a straight answer.

I’m looking for an answer to the following:

Are you susceptible while the sensor is within a creatures normal Gaze distance (usually 30") but you are not?

What if you and the sensor are both within the range of the Gaze, but you are only viewing it via the sensor (looking away, eyes closed, some sort of curtain or wall in between, etc)?