19th century. Ostensibly from ab- (“off”) + wimmeln (“to teem, to move in a confused crowd”). The meaning could perhaps be understood as “to keep such a crowd away, move out of it”. However, a more satisfying interpretation as “to wave aside” can be based on cognate Low German wiëmeln, wemeln, which also has the sense “to wag, wave”. Compare German abwinken (“wave aside”), abwiegeln (“appease”),…