Assistance needed with parsing a 32-bit flag - bit-manipulation

Question

I'm working with a 32bit signed int, that should contain true/false flags for 24+ items, starting with an id of 1. So my first assumption was that each bit corresponds to its corresponding item item id. So to start off, I simply did
(flag_int >> item_id) & 1
And this worked - mostly. For example, starting with a flag int of 125831406, the expected result(left) compared to the actual result (right)
1 true true
2 true true
3 true true
4 false false
5 true true
6 true true
7 true true
8 false false
9 false false
10 false false
11 false true <<
.. ??? false
22 true false <<
23 ??? true
24 true true
25 true true
26 true true
The trouble is, not every flag ends up with known discrepancies, and when it does, it's not always on the same id, and the number of discrepancies always seems to vary between 1 and 2.
So this tells me there's some other value at play. The good news is that there's two possibilities that I know of. First, is the entry id - which in the example is 307, and second is an additional 0/1 flag, which in the example would be 1.
The bad news is, that I'm woefully deficient in bitwise operations when it comes to flags, and my attempts have been all for naught. So while I certainly don't expect the "right" answer, some ideas on what to try would be most appreciated.

Answer 1

The purpose of these flags was to determine whether or not certain parts of a character should be hidden, by the type of headwear they were wearing. Each ID identified a character type, and each item had two Flag IDs - one for each gender.
To avoid any extra variables - I elected to use the "Ears" flag - because unlike hair, or other parts, it should've been the easiest to spot, with the lowest chance of additional complexity. I mean, every character has ears, and only one style of ears - so it should've been pretty binary.
The discrepancies - despite how much time I spent making sure I was getting the most accurate results, were embarrassingly easy to explain - because it had nothing to do with the flags, and everything to do with the traits of these characters.
One character type of each gender would ignore their flag, because their ears were part of the base mesh, and couldn't be hidden.
two more character types- both genders, seemed to defy their flag, only because their ears weren't considered ears, so their display would be handled by a different flag.
So anyway, that was the problem. If I would've simply taken another look at the mesh of those character types, I would've saved myself a ton of time.