What's a noun to describe the state of blinking?

You could use the word animation, as below.

Default animation: Blinking / Off

I don't like the answers "constancy" or "stable" they don't convey the essence of the domain you are looking for. Since you are using short phrases rather than fully grammatical sentences what is wrong with:

Default color       --- Red
Default brightness  --- 90%
Default blink       --- Off

You could also use:

Default blink rate  --- 0 for off, 5 for 5 blinks per secs.

It isn't really correct, but it conveys the meaning is spades. In computer user interfaces generally speaking the latter is much more important than the former.