"In line," meanwhile, suggests a line of people, any member of which is, well, "in."
But if we get pedantic we accept this will never satisfy the definition of a geometric line and the Brits were right all along to call them queues.
You're always 'in the' queue (or queuing) though, not 'on' it. So if you must call it a 'line' or a 'line-up', I sympathise most with 'in'.
But turns out it isn’t.
(Edit: Elaine, not Ellen. Thanks for the correction)