68 Camaro

The driver side sits about 5/8" lower than the passenger side. This is measured at the rear corner.

Front doesn't look off to me...just the rear.

Pretty much a stock rear suspension setup.
12 bolt rear end
Single leaf springs
regular shocks...don't know which ones.

Is there adjustability in the rear suspension? What do I need to look at for the possible cause?

you need to look for obvious things. bushings etc...

has the car been in a rear end collision?

Is the rear lowered 2" also?

I haven't seen any single leaf lowering springs, only multileaf. It could be your single leafs were de-arched and that could account for the difference, or they are just fatigued. Hotchkis drop springs are the in-option for rears.

I had the same issue with my 68. Everyone was looking at the rear and all along it was the front of the car. Check the distance from each wheelwell on the front to the ground. You will probably see a difference. The problem with mine was the front coils were not inserted in exactly the same position. I got a set of Z/28 coils and had them installed properly and now she sits level, and perfect on all corners.
Check that first, you might be surprised.

And after you've done all the above, just be prepared to deal with a 40yr old car not being perfect :). MANY of our cars don't sit perfectly level in the back.