Yup, it's the Steering Damper. P/N 45700-14010 MSRP $175.54
I'll look in my '88 TSRM and see if there's any testing info.
EDIT: The only thing I can find is the torque spec. The two bolts for it are supposed to be torqued using 20ft lbs and you're supposed to use thread locker on it.
If you know your ball joints, bushings and alignment are in good order, yet when you hit a bump on either side of the car the wheel tries to turn it may be the damper. The damper shouldn't cause the steering to pull one way of the other (unless it's seized). Perhaps someone wants to call up their friendly Toyota service dept. and ask for any tips to check it?