Matt,
Pad squeal usually comes as a result of oscillation of the pad material against the rim sidewall under braking -- the pad catches, slips, and catches again. This cycle is usually what results in noise (though occasionally it can be caused by a poor match of pad surface to rim...old MAFAC 4-spot and even 5-spot black pads were notorious for the squeal even when used on other brakes).
Toeing the pads in reduces oscillation and noise. If your brake arms are worn or already flexible by default, then more toe-in is called for.
If one of your pads is held less securely, that is where I would look first to find a source of squeal. Look carefully for any mismatch in size or for something that is keeping the assembly from tightening fully. Worse comes to worst, you may have to add a bit more toe-in on that one brake to reduce noise, but I'm betting the most likely cause is a loose fitting, based on what you've told us.
Yes, the spherical washers have to be mirrored as shown in the instructions to get the full range of toe-in.
On the rear left brake the gear shift mechanism located.
I didn't remove this.
Played safe.
Any tips for removing it and getting it back on in the same position?
When faced with a similar situation, I look for the gap in the clamp and mark its location with a piece of tape stuck to the handlebar right next to it. That way, when reinstalling, the clamp and assembly not only slides on the same distance, it has the same orientation. When finished, I just peel off the tape and all is as it was before.
All the best,
Dan. (...who appreciates the photo of the elusive spring)