The end at the top of the picture is the brake handle end. The other end is inside the sleeve and connects to the cam on the end of the rod.  But, as you can see, actually taking this apart to change the cable is puzzling. The large threads a the end of the sleeve don't appear to be functional. So again, if anyone has a similar Sturmey-Archer assembly on their tandem, I would appreciate seeing some pictures. Thanks again!

Looks more like a connector for a foot brake?

It is definitely stock as you can see from this picture from a book on the Fongers brand.  What I can't figure out is how to remove and replace the cable itself.  The whole thing looks like it was designed to be replaced in whole.  if that is the case, then I'm thinking I cut off the brake handle end, pull the cable through, thread a new cable back in and then recast the lead anchor. Seems like a bit of bother, though...

Looks like Sturmey Archer supply brake cables as a complete unit - cable, outer, adjuster and ends fitted on both ends ready to go.

This is the modern equivalent of what you are looking for I think.

You might be able to adapt a modern cable to fit. Check out the Sturmey website to find the part numbers for the different lengths. https://www.sturmey-archer.com/en/products/brake-levers-and-brake-cables

 

There certainly used to be brake cables with an end welded on, so that you couldn't replace the cable on its own - I had a BSA bike with effective roller-cam brakes that I had to discard because I couldn't replace the cable. I'm not sure I'd want to stake two peoples' safety on a blob of lead I'd stuck on myself. Would it be possible to pass the cable through  a bolt with a hole in the shank, as used for fastening brake cables to side-pull or V-brakes, instead?  

I am Secretary of the Veteran-Cycle Club and perhaps these members who have businesses specialising in restoring veterans cycles may have the part or solution that you require: Vince Warner of Colwood Wheel Works (a Sturmey Archer specialist) 01323848667, Christian Richards (Richards of England) 01482 738440, Chris Hewitt 01582 763622 and Doug Pinkerton 07778 429313. Latter two trade under their own names. We have a vast online library and expertise available to all members. Yours is a lovely restoration. Good luck.

Thanks to everyone for their input and insights. When I bought this bike, I have joined De Oude Fiets, bought Jos Rietveld's book (the section illustration above came from his book) and bookmarked every website and YouTube video I come across regarding Fongers and Dutch cycling. I joined this site so I could reap the benefit of your familiarity with the English components of the bike and hoping (who knows?) that maybe a Fongers tandem had found its way to England. Bottom line is they are really rare, especially with the outbreak of the hostilities at that time, so finding everything I need (not just parts but some tools also) to make this restoration  as complete as possible is a major challenge. Perfect for a retirement project...