Have a helper turn the steering wheel left and right a few inches rapidly while you watch the steering shaft and linkages. Look for the steering shaft going into the gear box turning before the output shaft coming out the bottom starts to turn. That play can be adjusted but it isn't usually a problem with GM gear boxes.
Watch the pitman arm, (attached to the output shaft on the bottom of the gear box). All of the other linkages should start to move as soon as that arm moves. If you don't see any play in the parts, have the steering system inspected at a tire and alignment shop.