[RPG] When can you see through your Ersatz Eye

You cannot end the effect early, but this should not prevent the wizard from speaking to the people around him.

The wording of the effect is very clear: until the beginning of your next turn. It is also important to note that the familiar does not move until its own turn, not during the wizard's, thus necessitating the full duration.

The wizard is deaf, but not dumb. Nothing about the spell or the defended condition prevents speech, although volume control would be impaired. The wizard could relay information to his companions, although he could not hear questions from them.

Now, there is one more point to consider. Can a character communicate during another character's turn? The chapter on combat, in the section entitled "Other activity on your turn," it says that you can communicate as you are able "as you take your turn." This does imply that you cannot communicate during any other turn. Since the familiar doesn't move until its own turn, the wizard will not be able to speak until the effect ends anyways. If the familiar is already in position before the wizard's turn in which he activates the effect, the wizard can describe what he sees at that time, although may speak more loudly or quietly than he intends from being deaf.

I see nothing there that implies it is a barrier to vision, just an active and utter absence of illumination.

You are quite right - there is nothing in the spell that says it blocks vision, just that the area is in Darkness.

However, a strict reading of normal darkness means you can't see through that (PHB p.183):

Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a subterranean vault, or in an area of magical darkness.

And a Heavily Obscured area is (PHB p.183):

A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see appendix A).

Which has been erratad as:

A heavily obscured area doesn’t blind you, but you are effectively blinded when you try to see something obscured by it.

So, darkness (magical or otherwise) creates a heavily obscured area. A heavily obscured area "blocks vision entirely".

Now, while it is clear what this means for "opaque fog, or dense foliage" is simple and straightforward - you can't see into this stuff and you can't see through it to stuff on the other side of it.

Applying this to darkness, however, seems to result in nonsense because, in the real world, darkness isn't a thing. In the real world darkness is the absence of light hitting your eyes from a certain direction. This can be because of an actual absence of light (underground) or because, even though the region is full of light none of it is coming your way (space). But this isn't the real world, is it?

So you have 3 options:

1. Darkness works just like it says in the book - you cannot see into it or through it. This would be really cool for a gothic horror campaign even though it would make navigating at night ridiculously hard.
2. Darkness (magical or not) works as it does in the real world - you can't see into it but you can see through it to illuminated areas beyond. I think this is what the rules intended even though they and the errata were poorly drafted.
3. Normal darkness works like 2. Magical darkness works like 1. There is no support for this in the Darkness spell description but this is how it worked in prior editions.

Its your world - make it fun.