I've had mine at Toyota a few times and they came back unable to find the source of the rattle.
In the end I gave up and jacked to car up to have a look myself, it's bleeding obvious why it rattles!
there is a shaft that the gear leaver pivots on, there are 2 plastic bushes between this shaft and the gear lever, and there is a washer and a circlip to stop the whole lot coming apart.
All this stuff rattles.... you can fill it full of thick grease and it'll stop, for a bit. ideally a replacement poly bush with tighter tolerances would resolve it.
Or remove the circlip and run a die down the shaft and reatin the lot with a nylock.
I did wonder if you could pack the entire assembly out with teflon tape, but seeing as it's a hinged joint I don't think it'd last very long.
I *really* don't understand how Toyota haven't figured out what the issue is or how to fix it, as I spotted it as soon as I wriggled under the car.