Can I combine the Blink Spell and a readied action to move around in the ethereal plane?

Question

Assuming I have cast the Blink spell on the previous turn and that I roll over 11 on the D20 for Blink at the end of my turn, can readying an action with the trigger "When I enter the ethereal plane, I run forward" during my turn allow me to move around for the time I remain in the ethereal plane?

If so, what rules, if any, govern my movement for the time I am on the ethereal plane? For instance can I walk through solid objects like walls?

If not, is it an issue with the wording of the trigger, or is there something restricting me from using my movement?

Answer 1

Yes, you'll be free to move but must return to within 10 feet of where you entered

From the description of the Ready action in the PHB or the Basic Rules:

First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.

Moving to the Ethereal Plane is certainly perceivable, so it works as a trigger. As per this QA, there is nothing about being in the ethereal plane that prevents you from taking a reaction.

As for limitations on movement, the DMG has this to offer on the Ethereal Plane:

A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don't hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings. This makes the Ethereal Plane ideal for reconnaissance, spying on opponents, and moving around without being detected. The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.

So you can move up to your speed, you can move through any solid objects, and you can even fly, but you can't move through other creatures (or force effects). Unfortunately, Blink stipulates:

At the start of you next turn, and when the spell ends if you are on the Ethereal Plane, you return to an unoccupied space of your choice that you can see within 10 feet of the space you vanished from.

So you can spy through walls with Blink, but you can't travel with it.

Answer 2

You can use Blink to move in the Ethereal Plane

...because neither Blink nor the Ethereal Plane have rules that forbid movement.

In particular, the Dungeon Master's Guide states:

A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don't hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings. This makes the Ethereal Plane ideal for reconnaissance, spying on opponents, and moving around without being detected. The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.

However, Blink also states:

At the start of you next turn, and when the spell ends if you are on the Ethereal Plane, you return to an unoccupied space of your choice that you can see within 10 feet of the space you vanished from.

In other words, traveling through the Ethereal plane with Blink will not help you travel the Material plane, unless (as Jason_c_o explains in this answer) you are trying to bypass a 5' deep obstacle.

You can also use Blink to move through walls, get a brief look at what's beyond, and then blink back to your initial location on the material plane.