Chances are it is the steering intermediate shaft, which goes from your steering wheel to the steering rack.
You can see in the second picture the brownish residue which is the joint rusting and slowly small parts of metal wearing away. They also seize and wear in the telescopic part which can cause the same symptoms. You maybe lucky and Toyota may repair your car under warranty, even if it is out of new car warranty provided your vehicle is’t too old and hasn’t done too many km’s. We recommended one customer to do this and a week later we received a lovely phone call from customer thanking us for our honesty, as Toyota carried out the repair free of charge after we diagnosed the fault.