May be worn or broken ejector sear(s) or (more likely) 100 years of crud built up in the ejector train. Try taking the forend iron out of the wood (carefully!), then soak the entire forend iron assembly in laquer thinner or similar solvent for a couple of days.

DO NOT TRY TO DISASSEMBLE THE EJECTOR MECHANISM!!! This is a job for a Parker-experienced gunsmith only - there are many small parts and some can actually be reinstalled backwards, like the small brass clips on either side of the ejector rails, which will go in but when the forend is put back on the gun, will not work properly, a major PITA after all that work! If thorough cleaning doesn't work, seek professional help. Botched Parker ejector repair jobs are like bad-running vintage Jaguar cars - aggravating and expensive!

Also should have mentioned that part of the problem could be weak or broken springs, compressed over time but seldom released by using the second set of bbls.

I would also add that the other forend may be interchangeable with both barrels. That way if you want to use the barrel set in question you can just use one forend, until you can get the other repaired.
Have you checked to see if the working forend will install and work with both barrels?

That would be great. I can wait.

I would recommend sending it to DelGrego if you want expert repair and service.