I also have a 68 conv. It sounds like it mihgt be coming from where the "header bow"(the part that rests on the windshield)attaches to the siderails wher the release handles are located. There can be a lot of movement in this metal on metal area. Thats just one guess out of many! I just had a new top and weatherstrip installed. But first I sanded the frame, treated the surface rust, replaced the tack strips,added new hydraulic fluid,adjusted the frame linkage and put a couple coats of satin black on it.
68 327/PG wht/blk conv.