i,
had a very similar problem recently on my mc2 aerodeck recently which took days/ weeks to source.
At first thought the source was low down and applied mastic to various seams but still didn't source it. Eventually, (after drying the area up every day) realised that the water was entering quite high up, probably inside a sealed interior panel.
On my car, the next highest panel upwards included the boot side widows so had a look and the seal to the window looked perished on the top edge, so applied mastic to that top edge ( you need to apply masking tape to the painted areas around before you do this) and after a few days the leak stopped. In your case this is complicated by the the rust around the hinges but still, look higher up than you might think for the source of the leak......