One thing you can try is acetone (real acetone, not nail polish remover) on a rag to do a quick wipe and remove any film on the brake tracks. Often variations in brake traction because of oil or wax films on the rims are the initial inputs that lead o resonance.
My commuter develops terrible squeal, with a bit of shudder the morning after riding in the rain. Fortunately the system is very rigid, so whatever causes it wears off quickly enough. If you have a garden hose, and a flat place to ride, you can soap up the rims with a concentrated dish detergent solution (not straight soap) and ride in circles dragging the brakes to burnish off any film. Then rinse complete and ride it dragging the brake a bit to dry it off. Then road test and see if anything changed.
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