On a 'checkout' the person being looked at completes the manouveres that the FI requests, to me that shows that the FI is in command...
But that's the whole point -- it's
not about actions
indicating which one is in command. It's about
agreeing which one is in command before the flight. There is no reason in principle why a check pilot must be the commander, but most check pilots who are FIs would expect to be in typical club circumstances.