I wouldn’t allow “when I blink” or similar and then blinking as soon as your turn is over either. Again, turns aren’t a thing in the fiction, so the character can’t blink when one ends any more than they can use one ending as a Ready trigger. It would have to be something that occurs in the game world, like “any of the monsters move” or as someone else suggested “Lancelot attacks an enemy.”
I don’t find the argument that you use the magic action to cast the readied spell compelling. It says you “choose what action you will take in response to the trigger,” so you are using the magic action when the trigger occurs, not when you Ready the spell. What is more convincing is the argument that, since you expend the spell slot when you take the Ready action, this could bump up against the “one spell with a spell slot per turn” rule. But since the example in the OP was casting with a staff, no spell slot is being used. So, again, I think this technique is valid and would allow it, but it is risky and I would have any intelligent enemies try to disrupt the character’s concentration before the trigger occurs.