Yes I have a multimeter and almost everywhere reads open loop.

On the bridge there is a metal wire across the adjustment screws with some occasional connectivity between the post holes and the saddles. On the tailpiece i can also get some occasional connectivity from where the string ends sit to the post hooks. I will look more closely later with a better light and a magnifier.

What is probably most important is getting connectivity from the earth wire to the tailpiece post as that is harder to fix once its in. So will give the tailpiece post a good scrape to remove paint. Maybe some solvent could be used to carefully remove some selected bits of paint.