My S500 Coupe does not have a shock warning light.Probably not just them. Until you inspect all aspects of the rear suspension, you won't know for sure. As a minimum, you need to change the accumulators, and flush the fluid. If they are bad and were ignored by the previous owner, there's probably other problems that they ignored. Bad accumulators will put unusual stresses into the rest of the suspension, especially the shocks, and their mounts. Bad accumulators essentially make the rear suspension solid.
Is your shock warning light lit on the dash?
This car has only 69750 miles, and has not been driven in 6 years. Where is the location to flush the old fluid and to put new fluid in ? What kind of fluid is recommended ?The accumulator does the "shock function" . The "shocks" are like hydraulic rams on excavator.
You will need to flush out all the fluid-Do a fluid exchange.
I can relate to this situation.There isn't anything to be learned from a visual inspection of the accumulators. Mileage isn't controlling, age plays a role. Fluid level? Often folks top it up. It might drop when the accumulator initially fails, but it will hold after that. Any bushing/mount in the rear suspension could clunk, check them all. If all ok visually, suspect upper mounts, which can fail due to age alone.