If all else fails maybe go so far as to securely strap a camera under there?
May have to do it a few times and aim it at various components each time.

 

I was thinking of doing exactly that with my gopro. I am in Puerto Rico until next weekend but intend to do it when I get back. I have my shop changing all the shocks to KYB for good measure. Even tho the current shocks seem to be fine, with 70,000 miles on them and being 31 years old, I am sure new shocks couldnt hurt!

 

Change your shock absorber, it's your problem. Kayaba it's good for xj40.

 

I have new KYB shocks being put in both the front and back. I will report back once I have the car back, wish me luck!

 

Finally figured out what the issue was! The passenger side rear exhaust pipe that goes over the rear axle had been modified by the previous owner at some point. It looks like when they welded a new pipe, they did not bend it enough because it was hitting the link over specific bumps and causing the knocking. I am so relieved to be in a quiet car again!

On a separate note, I am selling the front and rear shocks if anyone wants to buy them. Only 70000 miles on them and they turned out to be fine but since I bought the new KYB's, I figured I might as well put them in. PM me if interested!