Well, it took 5 days for Toyota to get a new spiral cable for my car and today I just got my Solara back from Toyota service where they installed the part. The clicking sound I first described is gone (at least for now).
The reason I can't be sure its completely and really fixed for good is because yesterday I installed my new OEM mud guards (they look great!

). Anyway, while installing the front set of guards, I had to rack the steering wheel from lock to lock twice to get access to the front wheel wells. Much to my surprise, the next time I drove the car the clicking sound had now completely disappeared. I guess turning the wheel lock to lock a couple of time had corrected the problem in the spiral cable in some way (at least temporarily). No matter what, I was still going to have Toyota install the new spiral cable they ordered for me.
At any rate, I hope this problem is now gone for good and I can really start enjoying my new car.