It seems to be getting worse, Im more aware of the steering wheel pulling left and right especially noticeable at lower speeds. I can see the front of the car going back and forth too.

What am I going to have go kablooey now?

Tires? Steering rods? A bad wheel? Motor or transmission mount?

Basically just a firm grip on the steering wheel and it goes by itself Im not correcting for it so whatever it is is pulling itself back?

 

Is it actually vibrating at speed, or does it just seem overly sensitive to variations in the road surface, or seem to wander on flat surfaces?

 

It could be just over sensitive to our beat up streets in the city. I have to think of where theres a street thats real smooth to check that.

I should include, if you gas it to hard on a wet street (or just not real gently) the car tries to pull left. Well no it does pull left. In my mind I think the steering wheel turns left then right during this shaking.

 

If it goes left or right during accel/decel, first things to check are the inner and outer rod ends for the rear toe links. If they are bad it will make the car very squirrely. The center link is one piece with both toe rods going into it, and if it is the original one, it is very easy for the assembly to get loose, but is also easy to tighten up. Here are some pics -

This is one tie rod end out of the center piece, the threaded part can work it's way loose and if it unthreads all the way you are going for a wild ride.
http://s790.photobucket.com/user/***...F0518.jpg.html
(The plastic ring goes between the threaded piece and the ball end)

This is the side that was loose on mine, only had one thread left holding it together.
http://s790.photobucket.com/user/***...F0517.jpg.html

This is what it looks like when threaded all the way in(btw, the rubber boot presses on like a ball joint boot)
http://s790.photobucket.com/user/***...F0516.jpg.html

I just pulled mine apart, cleaned everything, regreased it all and put it back together. I just used a hammer and punch to rotate the rings using the dimples intended for whatever special tool gm used. I tightened it till it (the rod) had some resistance to rotation, and I check it every now and then. If the outer tie rod ends are worn out, you will have to purchase the entire assembly, which will be a later version, because this early version has been discontinued.

 

Getting each wheel off the ground and checking for play in/out on the front/back of the wheel will reveal any loose front tie rod ends/rear toe rod ends.

 

Can I see these rod ends in the rear easily once the tires are off? Is this what Im looking for ? http://www.ebay.com/itm/MEVOTECH-MDS809-Center-Link-/301009998558?pt=Motors_Car_Truck_Parts_Accessories&fits=Model%3ACorvette&hash=item46159812de&vxp=mtr

 

No, that is off the front of a vehicle with a traditional style steering with pitman arm/idler arm, etc. (C3 corvette, before rack and pinion)
This is what you are looking for (looking from the rear of the car)-
http://s790.photobucket.com/user/***...F0743.jpg.html
It will be a little harder for you to look at if the spare tire carrier is on. It is directly above the rear leaf spring. First step though is getting each wheel off the ground and trying to turn the wheel left/right as if trying to steer. There should be no slop anywhere.
The rod ends are easy to see once the tires are off. There are inner and outer tie rod ends on the front, but the inners are hidden within the bellows on either end of the rack.

 

Thanks wouldnt you know it Photobucket is down. I can look at it later.

The front inner and outer tie rods I get, my other car has rack and pinion too. The rear I hve to learn from the beginning.

What I did today, was while I was stopped at a light when it turned green I took my foot off the brake and let the car crawl 5 or 10 feet with my hands off the steering wheel. Not far away of course.

Just crawling at a few miles an hour if that I watched the steering wheel go left about a half inch, then go right back to the right. Did that about 3 times in 15 feet I guess. A small pause before it went left right again each time. Maybe Im looking for a problem where it doesnt exist but I have to wonder. Its my first Corvette I guess Im getting where I want everything ti be right on it

 

I recall you mentioning in a post that your car was on a lift at firestone - has the alignment been checked?
If it is a bad tire it would get pretty bad at speed if it could move the steering wheel that much moving slowly. Generally, if there is a little too much toe-IN (wheels closer together in the front) on the front wheels, the car will feel VERY responsive to steering input, and will dart back and forth, too, along with over reacting to ruts in the road. If there is a little too much toe-OUT (wheels further apart in the front) on the front wheels, the steering will feel a little sluggish or slow to respond, and the car will slowly wander around or drift left or right. If the caster is off on one wheel, the car will ALWAYS pull to the side with the most negative caster. (upper ball joint further forward than it should be) It kinda sounds like maybe you have a little too much toe-in, which will wear the outside edges of the tires more than the rest of the tire. Caster doesn't usually cause uneven tire wear unless it is way off.

The rear suspension is kind of neat on the C4's. It is a 5 link setup, and one of those controls the yaw (model airplane language, not sure what else to call it). It is similar to the rack and pinion on the front, just at a fixed setting. So, if the ends get play in them, you get the rear end steering the car too, and it shows up a lot when you accelerate and decelerate, and when you drive along ruts in the road.