Object moved in straight line, "disappearing," then coming back, shimmering brightly, not in reflective pattern, very high in sky

At approximately 10:45AM I observed an object in the sky from my kitchen window in my 3rd floor apartment in the Edgewood neighborhood of New Haven, CT. The object caught my eye because it occasionally shimmered very brightly. It appeared very small because of how seemingly high in the sky it was (above where I would expect to see an airplane). It moved slowly in a straight line, much like when you see a satellite at night. I watched from the windows and lost site of it several times, it seemed to disappear into the blue of the sky. Then it would come back along the same trajectory that it had been traveling. It appeared to be a rectangular shape, in an upright position. However when it shimmered it was so bright the shape could no longer be understood. The shimmering did not seem to have a consistent pattern. It would occasionally shimmer at seemingly random intervals. Today's weather was warm with a bright blue sky, not a cloud in sight. This made the shimmering all the more confusing as it did not seem to make sense as reflection from the sun. However, I do wonder how the objects extremely high altitude would affect my eyes interpretation of reflections. It continued moving at a consistent speed, along a straight trajectory until I could no longer see it through the windows.