Victory! Glorious victory is mine! Along with all the bounty and spoils!

Turns out, it was the housing. Before realising that, however, I punched the spring several times. One time, I dislodged the spring on one side, without noticing it. After about a half hour or so, I realised it. Then I trimmed about three inches from the last set of housing. That did the trick!

Tried punching. All it did was change which caliper would fail to return.

Either you have the bolt that fastens the brake to the fork or stay bridge too tight or the spring in the brake is weak or broken or perhaps not hooked onto it's holder (boss), or you simply need to lube the spring/caliper pivot points.

So try first lubing the pivot points.

Then check the spring to make sure it's where it is suppose to be and that the spring tension is correct. Then only after you do the what I talk about in the next paragraph below and that fails then pop the spring out of the boss and make sure the spring and the caliper where the spring was is clean, and then put some grease in between the spring and the brake caliper. Then reassemble and work the caliper and see if that works better.

Then loosen the front first nut on the pivot bolt a bit then loosen the nut behind that one just a little bit and check to see if the brake will function better. It the brake functions the way it should after loosening that back (pivot anchor bolt) nut just a small amount then simply leave the back one alone and tighten the front while trying to keep the brake centered, once tightened then do the punch method to relign the calipers. Some manufactures actually have torque specs for these nuts, is so it's obvious you need a torque wrench to do this properly.

You can also get a degree of centering by placing a wrench on the rear pivot anchor bolt nut and move it left or right depending which way you want to go.

Summary; I think your pivot bolt is too tight which I address above, but I'm not there so I can't really tell what's happening.

Brakes are working as of maybe an hour ago.

Rekmeyata,
Thanks so much for that super detailed reply.

I apologise for the mix-up. Strange that my post ended up being two separate ones. Must have had something to do with posting from both my iPhone and my computer. /shrug

if not the <C> star washer in #9, there are spring steel outside star washers Made.
more common regular machine hardware..
that will also work.. NB, an inside star washer, is also made..toothie-ness is inside

Glad to hear your problem has reached its resolution , Raleighsport . Well done .

The toothed washer goes between the caliper and the frame:

http://www.os2.dhs.org/~john/brake.jpg

Grease on the spring where it anchors on the caliper prevents it from hanging up due to friction.