This should work
Let's go through step by step and I'll go through every requirement
As long as he has a 3rd level spell slot, a free hand, and can speak this is no problem for your wizard.
This means at the end of your turn there is a 50% chance that you will be on the Ethereal Plane until your next turn starts.
To cast banishment and hold the magic (the crux of the Ready action for Cast a Spell), he will need something he distastes which should be fairly easy for your wizard to figure out. The trigger for the Ready action must be perceivable which entering the Ethereal Plane certainly is.
While on the Ethereal Plane, you can see and hear the plane you originated from, which is cast in shades of gray
Let's assume you rolled an 11 or higher on blink (if not you have to wait until next round for this plan to work, and your spell slot is expended). Banishment has a different effect depending on the plane the target is on. Since your wizard is on the Ethereal Plane due to the blink spell (reactions take effect after the trigger), and his native plane is the Material Plane, he will be transported back to the Material Plane until the spell ends as long as he fails the save.
You may be unable to willingly fail a saving throw in 5th edition and if your wizard succeeds, he will have to try again next turn with a new 4th level spell slot.
All you need for this is an action, which you get on your next turn. Since you are already on the Material Plane, blink does nothing at the start of your turn. (emphasis mine)
At the start of your 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.
There is no such thing as a "free action" in 5th edition, but ending concentration takes no effort on your part.
You can end concentration at any time (no action required).
When he ends his concentration (as long as he does so within 1 minute of casting the spell), banishment returns your wizard to the space he cast it from, on the Ethereal Plane.
If the spell ends before 1 minute has passed, the target reappears in the space it left or in the nearest unoccupied space if that space is occupied.
This isn't quite low-level etherealness since your return method of banishment has an undetermined destination whereas etherealness ends by returning you in the spot you occupy. Banishment places you in an undisclosed location and as such, your GM decides.