Transform Constraint And Keying bone

(I think)

I'm also having trouble understanding what the 'local' and 'relative' options do, and the linked thread didn't help me understand. Is there a detailed explanation anywhere?

Oops, someone should have replied to the OP, sorry! We also need to update the documentation.

When Local is checked, the constrained bones' local transform is modified to match the target bone. When unchecked, the the constrained bones' world transform is modified to match the target bone.

When Relative is checked, the constrained bones' transform is modified by adding the target bone transform (ie the new position is relative to the constrained bone's position before the transform constraint is applied). When unchecked, the the constrained bones' world transform is modified to match the target bone (ie the constrained bone's position before the transform constraint is applied is overwritten).

Does local also only look for changes in the local transform of the target bone (can it be used to prevent the constrained bone from changing due to transforms applied to the target bone's parent)?
I have a constrained-bone, a target-bone, and a parent-bone. Both the constrained-bone and the target-bone are children of parent-bone. The constrained-bone has a transform constraint on it that targets target-bone and has rotation mix set to 100%. Can I use local to make it so, when I rotate parent-bone, constrained-bone isn't affected by the transform constraint (it only rotates because it's the child of parent-bone)? constrained-bone would still be affected by the transform constraint if I applied rotation directly to target-bone.
I've been unable to achieve this so far.

Can I use local to make it so, when I rotate parent-bone, constrained-bone isn't affected by the transform constraint (it only rotates because it's the child of parent-bone)?

With Local checked, only the local transform of the target bone is copied to the constrained bones, which is what you want. Give it a try, it's a lot easier to see how it behaves. If you can't make it work, post your project file (images not needed).

Here are the bones of my project where I'd like to make use of the relative option. I want to be able to rotate spine while keeping skirt front 1 counter stationary relative to skirt front 1.

You have a bunch of things going on, I can't tell which constraints are actually useful. Skirt Front 1 Counter has inherit rotation disabled. Turn that back on by checking Rotation, then I think it behaves like you want:

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