WAIT...YOU HAD ME AT "THE SQUIRRELS"....Although I am hoping these are wild squirrels (because that would be even funnier), your phrasing makes me think you have squirrels as pets? LOL I must know! Did this all happen on the same day?
Today, I must have done something to irritate mine (?) because she lunged at my finger and grabbed it fully with her beak, but she applied ZERO pressure---it was like the equivalent of a baby holding someone's finger for a few seconds--and she was super nice right after that..it was odd. It had all of the body language of her "I can't believe you left me bites"...Yet it was a TOTAL fake-out without any pinching ( I was so dang tired that I didn't even move to doge it because my reactions were in the toilet lol).
I guess it all is communication when you think about it...Mine is very gentle too for the most part but the following types of bites have occurred:
When I first got her she would sometimes nip at me--fingers bleed easily, so that happened occasionally during early step-up moments (possibly fear) and then when she decided she was going to stand on my shoulder without permission early on- AKA "I DON'T WANT TO LISTEN TO YOU BITES."
Then there were the "I'M UP TOO LATE" bites that I discovered when I kept her away from her cage at bedtime because SHE moved her bedtime back without telling me lol. She bit to go back to her cage because that had been her punishment for past biting but she couldn't tell me she was ready for bed without bobbing in her cage the way she does each night lol.
The most "angry" bites I have gotten were within the past month or so because I left town for 3 days and left her with my parents. They didn't bleed but they were still hard (I posted those--the arms) and she was obviously mad at me. I walked into my parent's house and she was super loving and happy for about 3 minutes. After saying hello, she stood on my arm and LITERALLY YELLED/RANTED at me for 10 more. After the rant, she bit me a few times and then off-and-on for probably 5 days after (mostly when I had to leave for work or the store )...="DON'T EVER DO THAT AGAIN' bites.
She has ever bitten me her hardest because I would likely have ended up in the ER.
They do have SURGICAL precision with their beaks.
Mine always preens my face and eyelashes (I KNOW I COULD LOSE AN EYE...SPARE ME THE TERRORS/WARNINGS...I know she could get scared and accidentally bite etc). ...That having been said, she is obsessed with preening my eyelashes and I had never encouraged this (I was terrified when she first tried it for the first time, but if I don't let her, she almost gets offended/sulky).. It is weird...and I have kind of given up resisting at this point.
Stupidity aside, she is always VERY gentle and she doesn't want to be near my face when she mad/nippy, so I have taken my chances. She doesn't want to preen me unless she is in a good mood. When she has tried to pick bumps off of my skin, she has pinched harder by mistake a few times and my reaction + the word "gentle" has improved her judgement TREMENDOUSLY.