My eclectus book shows several different types of nest boxes, hollow logs, "L" shaped boxes.  Only information that it gives is that the size and style of the box is often of little importance as long as there is enough room for two adult birds inside.  Since eclectus sometimes mate inside the nestbox, this makes sense.  I'd think that a box 12" square would be about the right size for them, providing the hole is up high enough that the young chicks can't fall out.

I found this for you but couldn't post it til now.

 

I have been trying to think if we have ekkie breeders here at BB.  I don't think so. I looked on the internet and found, at Lexicon of Parrots, a little info about breeding.  The nestbox size is 12 x 12 x 32 inches, but they don't say whether to lay it down on the long side or if that is depth.  I will guess that you lay it on the long side so they can climb in and out.  Entrance hole is about 4 inches.  You can make the hole smaller and let the birds enlarge it to whatever size suits them.
If this is your first time to breed, you sure need to get a good book on breeding them so you won't make a fatal mistake with them.  Also you need to be prepared to handfeed the babies if the parents won't. Someone needs to teach you before the babies hatch.
Ekkies will lay clutch after clutch of eggs until they have depleted their calcium.  So after about two or three clutches, you may have to separate the male from the female and remove the nestbox so her body can rest and renew her calcium levels.
She will lay 2 or 3 eggs per clutch. Incubation lasts for 28 to 30 days.  Then the babies stay in the nest for another 70 to 80 days unless you remove them for handfeeding.
I got all of this info from the internet by typing in  Breeding Eclectus parrots in my browser.  Much, much more information is available to read by doing that.
Annie