Three years ago, my wife and I adopted a cat from a coworker's relative. She's a very small calico/manx, and she was about 1 year old when we adopted her. We have no reason to believe she has ever been abused, either directly or through neglect. We were told when we took her in that she was shy, especially around guys. We've since discovered that was quite the understatement.
We have another cat, slightly older, also female. When we took in the calico, we kept her in our bathroom for a few days to help her get acclimated to her new environment before introducing her to our older cat, and she was terrified. She yowled, jumped around the bathroom, then eventually settled in the best protected spot in the room (which in this instance was behind the toilet), trembling the entire time.
After a few days, we let her explore the whole apartment, but she didn't move until we were both at work, and even then it seems all she did was resettle under our bed. At no point did we force her out from under the bed, or encroach on her hiding place. Our plan has always been to wait until she feels comfortable enough to approach us on her own, but it's starting to look like we aren't approaching this correctly.
As I said, it's been 3 years, and there's been next to no progress. In these 3 years she has taken up residence under the bed, behind a pile of boxes in the closet, behind the washer, behind the dryer, inside a chair, and inside our couch. This diminutive little creature can squeeze into every nook and cranny in the apartment, and seems resolute on living exclusively inside them.
The exception here is at night, if things have been calm and quiet for a while, she will occasionally jump up on the bed next to my wife (she feeds the cats in the morning, so their relationship is a little bit better). If we're slow and deliberate, we can pet her a little (and she purrs when we do), but she'll stare at us the entire time we aren't touching her, and if we make any move beyond slowly moving an arm towards her, she'll dart off to her current hiding place. Likewise, if we sit on our couch for long enough, on rare occasions she'll come out and stare unblinkingly at us from across the room, but if we move at all it's back to the hiding place. She started doing both of these a few months in, which we thought was progress, but that's the last improvement we've seen.
She also leaves her hiding places at night when we're asleep (we can hear her playing with our older cat). Our two cats get along well, and we don't think the calico feels threatened by the older cat. If she hears either of us move though, she'll immediately hide.
I understand calicos are shy, but we also don't think our cat is happy like this (and personally, I'm pretty sad my cat is so scared of me...). We know she prefers being in the open, as she is almost every time she hasn't heard my wife or me in a while, but she ends up spending most of her life hiding. She's currently living in our couch, and on a typical weekend, she'll spend the entire day, every day, inside it, sprinting out occasionally to go to the bathroom then sprinting back (on weekdays the hiding starts the instant one of us gets home).
Is there anything we can do to help her feel more comfortable? We've bought her a cat tower taller than us so she might not feel so exposed, which we've seen her in, but she doesn't seem to feel any safer in it. We've also taken her to the vet for regular checkups, and she's always been healthy. We're perfectly happy being more patient, but it seems like we haven't made her feel safe enough with the status quo.
(I don't think this is a duplicate, since in this question they'd only had their cat 10 days, and in this question, their cat was "further along" than ours. That Q/A seemed focused on making each encounter build more trust, but at this point we just want to encourage more encounters)