Harry,
Thanks for these suggestions
I don't really notice it anymore ! I take it for granted.
It is not severe, just annoying as it waggles.
I'll try what you suggest but have my doubts how meaningful the test is.
For the benefit of other readers.
The tailgate is connected to the struts in the normal way.
The motorised assist, via a 15 inch long rod, is connected to the tail gate quite high up in relation to the hinges.
As the door is only assisted on one side, the nearside, that, in itself, could cause the waggle.
However, I cannot believe Toyota allowed such an ineffective design to go to market.
I could disconnect the rod but I am very cautious that the full load of the door will be borne by only the struts and , I, personally will need to take the excess load !
I may have my mechanic take a look as he will be able to carefully, and safely, prop the rear door open as we 'play'.
I have previously oiled the struts and greased the hinges, but to no effect.
Lubricating the struts is not made easy by having the rods, when extended, on the lower part of the assembly !
Your reply has piqued my interest again ....