I've just fixed the rattling.
From looking at the rear of the targa where it inserts to the car, the two bolts that held it in place came totally off. I tried to remove the linings, but from the glue and seals, no wonder they need to be replaced.
Luckily I fastened the bolts without resorting to removing everything. What I did was flip the plastic covering so that I would be able to reach. The plastic is somewhat soft, I think if you heat it with a heat gun or blow dryer, it would be even softer, but becareful not to flip so much that you break this off. Then I slowly and carefully turn the screws manually, by hand and sharp nose pliers. Once its furthest in, I used a 12mm wrench and tighten the bolts down. Problem solved.