Henshall says 川 acts phonetically in 順 to express “comply” and lends an idea of “flowing down”—and by association kowtowing. The character 順 originally referred to someone who bowed his or her head in compliance. This gave rise to the meaning “follow,” and then to “order” or “sequence.”
And then Henshall makes this great point: “Note that the English word ‘order’ similarly has associations both with ‘sequence’ and ‘compliance.'” Meaning, we need to do things in order (sequence). And I can order you around until you comply!