I've removed everything removable from the main, centre part of the carb body (base of float chamber and venturi), but when I shake it, it rattles! There is something loose inside one of the inaccessible chambers or channels within the carb body. I know there is a tube hidden beneath the non-removable air jet - ie, the one marked by the central red arrow in this photo -

Sounds like that is where the rattle is coming from.
So... is this normal? Is there a hidden part that rattles when you shake? Or is there something rattling around in there that shouldn't be there?