Does Arcane Eye transmit information if the caster moves to a different plane?

Question

The description of arcane eye states that the eye created by the spell "can't enter another plane of existence." PHB p. 214.

Consider this scenario: a warlock casts arcane eye (perhaps using the Visions of Distant Realms invocation), creating an eye 30 feet away; subsequently casts demiplane; and then steps through the shadowy door created by demiplane, leaving behind the eye exactly where it was created.

What result? Is there any rules-as-written reason to rule otherwise than that the eye did not "enter" another plane, and so remains in existence and continues to transmit information across the planes? Or does the eye remain in existence but cease to transmit information? Or does it cease to exist? Or something else?

Answer 1

Yes. The caster can see through the eye from another plane.

The eye cannot move to another plane. This does not restrict the caster.

There is no limit to how far away from you the eye can move, but it can't enter another plane of existence.

The spell description does not indicate that it does not work when the caster moves to a different plane.

Answer 2

RAW nothing would happen to the eye or to the vision through the eye if the caster moves planes.

The sentence that you half quote reads as follows:

There is no limit to how far away from you the eye can move, but it can't enter another plane of existence.

There is no other limit on the whereabouts of the eye within the spell description, only restrictions on size of gaps or speeds.

As the caster is the one changing planes and not the eye, the above clause does not come into effect.

If the spell meant that both caster and arcane eye have to be on the same plane of existence for the duration of the spell (for vision), it would specify that (for example, with the last clause instead reading "but it must be on the same plane of existence as the caster at all times").