Unfortunantly the door drip wires do occasionally come loose. More unfortunant is that , unlike most Morgan repair tasks, there is only one way to make the repair. The wire must be resoldered. There is no glue that will work and attempting to weld the wire is just a bad idea.
If you are starting with new metal fit the door and make a deep scribe line around the leading edge. If the drip wire has only come loose then the correct location is obvious. In either case the metal must be sanded/ground clean for at least 1/2″ on either side of the wire location. Sorry; Paint repair is inevitable.
Next step is to “tin” the area to be soldered. Remove the door. Brush soldering flux on the area (better yet use Tinning Butter from Eastwood.com). Using a propane torch start at the top and work your way down. Get the steel just hot enough to melt 60-40 solder or, if you are using tinning butter, have it turn shinny. Scrub with a wire brush as you go.
Sand and clean the wire and then tin it all around, top to bottom.
Clamp the tinned wire on the tinned scribe line. Use small clamps. Use enough pressure to make contact between the wire and the steel and enough clamps to guarantee that there are NO gaps.
I prefer bar solder also available from Eastwood but 60-40 wire solder will work fine (not the lead free stuff!). Start at the top. Heat an inch or two until the tinning lead is fluid. Melt a blob of the bar solder on top of the wire and continue heating down the wire drawing the melted lead along as the wire and base steel get hotter. NOTE: the clamps act as heat sinks so be sure to focus some heat on them as you continue drawing solder down the wire joint.
After the solder is cooled remove the clamps and scrub the entire area with a thick paste of Baking Soda and water to neutralize the acids from the flux.. Forget this and your future paint job will fail.