[adouglas]

Been awhile since I owned a Ninjette, but...

On both of my bikes (GSX-R and R6) the rear wheel hub is hollow and has a big hole in it (between the spokes, facing the rim), presumably to keep water from taking up residence.

I can imagine a foreign object falling in there and rattling around when you spin the wheel. It wouldn't be in the tire (as noted, it's impossible to get an object inside the tire without deflating the tire first). It'd be inside the wheel hub.

But the hole on my bikes is so big that it'd soon fall out.

Again, don't know if this applies to Ninjettes at all... but it's all I've got. Sorry.

Suggest you remove the rear wheel and shake it/move it around to locate the bit. If you don't hear it, then it's not in the wheel at all.