Shutter explains it to the T.
This one is sort of interesting as I have had a similar experience....on a different brand vehicle.
Specifically, one of my Impala's.
These cars sit unused for extensive lengths of time and weird things crop up.
A few years ago, when I would start my 95 to move it about in the building, sometimes the steering would chatter, right through the wheel.....sound familiar?
Anyways, the LT-1 V-8 uses a camshaft driven water pump...no belt.
Because of its configuration and long sit times, I found it would decide to drool coolant on the power steering belt from time to time and upon startup, the pump would slip/spin a few times before the belt dried, making the steering chatter.
Strangely enouph, the pump would not leak with any regularity so I had to have it happen a few times before I caught it in the act.
And, it would only leak for a minute or two and then seal itself up (damn mechanical pump seals do that)
Anyways, you might want to remove the shield and look up fron the bottom with a good pinpoint light.....might be something from above.