my nut also makes this gentle beak clapping/chewing/clicking/snapping
1, when i am giving her a head rub and she is happy, the rest of her body is relaxed, her eyes may or may not pin, her head is side ways on or curled down so i can get them pin feathers for her, its a very gentle beak movement
2, when she has been startled or scared she will fly off hang of the curtains and i see this beak movement, but the body is stretched (what ever angle she is hanging in, mostly upside down) feathers all flat, faster beak movement, but it never lasts long
3 like your kiwi, when nut puts her whole focus into one area/object its never that good, that chewing sound is it like a snap/click??
when nut gives these *you are annoying me warnings, her head is bowed, but beak and eyes both point directly at her intended strike area, her head feathers are slightly puffed, and her cheek feathers are sometimes super puffed (makes her look really cute though)
another way of reading this, is the demand for a head rub, as the most common way for our birds to request one is with a head bow?
when your bird displays a warning, i would say walk away! find ways of making him come to you! the nut escalated her warnings into vicious attacks because i miss read a lot of nuts warnings as i made the mistake of only reading 1 part of her body language, and pushing what i wanted her to do