I have a beige female with ruby eyes, who does the head-wiggle depth-perception thing a lot. She's a biter, but not as bad as she had been when we got her (which was because she was pregnant, but we didn't realize until she had her babies). She only bites if my hand comes at her from the front, so I can pet her or pick her up from behind no problem.

My question/problem is this: When I hold her, she just kind of sits still, a bit nervous, but doesn't otherwise show any interest in anything until I put her back in her cage. I think that she's probably just a little freaked out because she can't really tell much about where she is, and it isn't 'solid ground' when I hold her. I know that holding her more often is probably the best solution, but I'm always worried that she'll get spooked and bite, and she's definitely the strongest rat I have.

I had a male fawn with ruby eyes years ago (RIP Basil <3) who also seemed to have poor vision, though he would nip if you startled him and grabbed him from behind, and he also seemed very disoriented when I took him out of his cage at first. I always made sure that I talked to him when I was about to pick him up (my logic being that if he could hear me, he'd know I was near even if he couldn't see me) and moved very slowly when I pet him or picked him up. I first fed him small amounts of yogurt from a spoon, and worked my way up to getting him to take food from my hand.

He was always rather...unactive. Mellow. He was a big boy, and his favourite place to be when I took him out was inside this ripped pillow I had on my bed. He'd crawl in there, snuggle up, and occationally waddle out for for pets and treats, and then go snuggle up again. It could have been because he was male and thus just lower-energy, and maybe your female is different, but some rats just aren't that interested in exploring.

Holding her with gloves is a good suggestion, if you're worried about her biting. It sounds like she may just need a little time to get comfortable and adjust to her surroundings. Have you had her long?

Also, sitting down and letting her sit on your lap for a while could be a good way to handle her more, without her feeling like she's so unstable from not having ground beneath her feet.