If a caster under the effect of blink enters the Ethereal Plane, does that break contact with the target for purposes of ongoing witch bolt damage?
The spell text of Blink (emphasis mine) states:
While on the Ethereal Plane, you can see and hear the plane you originated from, which is cast in shades of gray, and you can’t see anything there more than 60 feet away. You can only affect and be affected by other creatures on the Ethereal Plane. Creatures that aren’t there can’t perceive you or interact with you, unless they have the ability to do so.
You are casting Witch Bolt but you are not on the ethereal plane. Therefore, you cannot affect someone who is on the ethereal plane by the effect of Blink.
Furthermore, you cannot percieve or interact with someone who has successfully become ethereal through Blink. Witch Bolt does not specifically require sight, but I would definitely classify targeting someone with a spell as an interaction.
Furthermore, as Tim Grant suggested in the comments, several magical effects have the caveat that the work so long as you and the target are both on the same plane of existence. If the target blinks away, they are not. The general rule of thumb is that spells do only what they say they do, and Witch Bolt does not permit the targeting of a creature on another plane. (Spells that do, such as Sending typically mention that it is a capability of the spell.)
Witch Bolt tells you the conditions that end it:
The spell ends if you use your action to do anything else. The spell also ends if the target is ever outside the spell’s range or if it has total cover from you.
Being ethereal is not one of those conditions.
The ethereal plane overlaps the material plane so as long as you stay within range the magic continues to work. Going to a plane other than the ethereal is probably out of range.
To affect a creature on the Ethereal Plane, a creature on the Material needs “a special ability or magic [that] has given them the ability to do so.” (Etherealness spell, PH: 238.)
Descriptions of etherealness specifically call out that effects (notably, spell effects) don’t cross to and from the Ethereal Plane, unless they specifically say otherwise. Witch Bolt has no such language.
On the other hand, already-existing effects won’t be lifted from a creature just because it shifts to another plane. Which rule covers sustaining Witch Bolt?
Range to Ethereal Targets
It’s an interesting question whether being in a corresponding area of the Border Ethereal increases your range from a finite number to “other plane of existence.” The answer will depend on context.
A ghost that is 30 feet away is still thirty feet away if it simply switches to the Ethereal Plane. You would use that 30 foot range for any attacks on the ghost.
The caveat is, only effects or objects that can affect ethereal creatures can truly reach the ghost (doing it damage). Like most magical effects, lightning exists in either the Material or Ethereal planes. Ethereal creatures “ignore all objects and effects that aren’t on the Ethereal Plane.“ (Etherealness, p. 238).
But normal objects and spell effects on the Prime Material can never hit the ghost, because (for them) the ghost isn’t really there, just an image of it is. For practical purposes, the ghost is thus forever away to most things on the Material Plane.
The “Sustained Arc” cannot arc between planes
Witch Bolt does damage through a “sustained arc of lightning between [the caster] and the target.“ This arc exists either on the Material or the Border Ethereal. It cannot cross between the planes — it’s just another effect on the Prime Material that is ignored on the Ethereal.
This “sustained arc” in the spell description is as much a rule as the list of conditions that end the spell. If anything happens that makes that sustained arc of lightning impossible, the arc should be considered broken, and the spell ended. Put another way, the “sustained arc” clause should inform how we interpret the spell-ending conditions like total cover or maximum range.
Either the caster or the target moving to (or from) the Ethereal Plane would break the contact required by Witch Bolt.