I've got a very old 10-speed roadbike (1971 Motobecane) with side-pull "Weinmann Symetric" caliper brakes and those "non-speed-release" hubs — you know, the kind which requires 30+ minutes of fiddling around with how the wheel sits in the frame until it sits exactly vertically and horizontally parallel to the frame. However, I have problems with my rear brake flexing the top half of my rear wheel to the right side by about 1-2 millimeters when I brake. The wheel is as parallel to the frame as I can get it and it is (more or less) true; likewise, the distance between the rim and each caliper is roughly equal.

Does this mean that the brakes need adjusting?— if so, then how do you "center" the pull on these side-pull brakes? From what I can see (see attached photos), there doesn't seem to be any adjustment facilities besides for the caliper-rim distance, adjusting the brake shoe in relation to the caliper, or simply "pushing" the calipers to one side or the other. However, doing the last option doesn't seem to make any difference at all— in fact, it seems like they "automatically" get "pushed" back to their original position during braking.