REST API - json and chaining issues
Not everyone else use only the json, I find it easier to read and fix to use separate params ;)

I think the error is on the json you provide is not correct. Instead of:

["sequential"=>1,"return"=>"id,do_not_mail","external_identifier"=>777]

it should be

{"sequential":1,"return":"id,do_not_mail","external_identifier":777}