Drip rail on a '59?
Do you mean the "reveal molding" on top of the door at the base of the side window (when the window is up) atop the upper door fiberglass that has a thin extension that goes up the door post next to the windshield? Strangely enough, the service manual doesn't show any sealer used there. I don't have an AIM for that year, so I can't say for certain. My '57 AIM shows a bead of sealer only where an end cap (used to finish and secure the rear of the reveal molding) touches the fiberglass. My AIM shows a smaller retainer molding screwed into the fiberglass sill from the top with one screw, and the larger reveal molding attached, through holes in both moldings and then into the door fiberglass, using three screws... from the inside of the door horizontally toward the outside. No sealer is shown for the retainer molding
Or are you refering to a molding that attaches to the hardtop?
What was commonly used for this type of application was something called "dum dum" by the factory, or "rope caulk"... available from 3M at your local bodyshop supply store (grey in color). It is a body putty pre-formed into "rope" about 1/8 to 3/16 inch in diameter. Once applied, it can be smoothed along the sealed joint with a tool, removing the excess, similar to the way you'd glaze a window pane or caulk a bathtub, except only a little putty is left visible in the seam.
