Does the Robe of Eyes extend your vision while on the Ethereal Planes?

Normally the following rules on the Ethereal Plane apply (DMG page 48):

Visibility in the Border Ethereal is limited to 60 feet. The plane’s depths comprise a region of swirling mist and fog called the Deep Ethereal, where visibility is limited to 30 feet.

However, the Robe of Eyes states:

You can see invisible creatures and objects, as well as see into the Ethereal Plane, out to a range of 120 feet.

If you are already on the Ethereal Plane are you still considered to be seeing into it; does stepping into the Material Plane really suddenly lower your range of vision?