Found new Toyota part on ebay
https://www.ebay.ca/itm/304157352064?hash=item46d130e080:g:6UQAAOSw98thTCYY
Or internationally from partsouq for a few dollars more (shown in Canadian $)
So, where did this thread wind up?
Random pedal engagement = wheel bearings? Which I get sort of, since the front brakes are four piston, opposing, no slide pins.
I have a pseudo similar problem.
I will apply a constant pedal pressure, and can feel the entire vehicle slowing, releasing...