Yes there is continuity there. Check out the wiring in this diagram. All the GI strings go back to the same input from the transformer entering at J115.

Is fuse 110 good? Remove from the holder to test with your DMM.

There are no traces sandwiched in the middle of the board, only on the front or the back. Sounds like the fuse holder F110 will need resoldered.

You can label all connectors and take a bunch of pictures. Carefully unplug the connectors and remove the board. It’s a little overwhelming the first time but you can do it. As stated do not pull the wires, grab the plastic connector body only.

You can count the number of connectors and their locations so when you reassemble you can make sure you got them all. Take your time and be careful especially with the ribbon cable. Make sure all pins are lined up before pressing it on.

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Hmm. Someone can correct me but if you unplug J115 there shouldn’t be a connection between pins 2 and 3.

Something is going on with that connector and fuse 110. Was there previous work done there?

No, I wouldn't double up any other GI string with these additional lights. It's probably heat that killed this connector's header and adding lamps would not be a good idea.

What you'll need to do (eventually) is remove the board and desolder old header at J115. Solder in new header and replace J115 connector with fresh pins. This way you can see what has happened to the fuse connection. You can get a pin buddy to supervise you if you're not ready to tackle this step alone.