A possibly easier way to check, assuming that the problem is the shocker itself & not merely loose mounting bolts, might be to check the temperature of the shocker.
After a longish run the shockers should be warm to touch. If they are cold, then they have not been doing anything. I admit I have never tried this on a Healey, but in the transport maintenance game this is the best method of checking shocker condition.
On the other hand, after a longish run everything on a Healey would be hot to touch!
Loose bolts is much more likely. The most obvious symptom is a rumbling sound coming from the rear axle area. It is not uncommon to find the mounting holes worn into elongated slots by the loose bolts.