Hi from sunny and socially-distanced Australia!
Not meaning to hijack your thread Mad Doug, but looks like we're both on the same search, so I'm happy to provide a bit more background on the model. Best bike I ever owned was a 1956 Triumph Gents Palm Beach Roadster (like the one in my avatar pic), which I bought as a teenager in Bognor Regis for 10 bob a week on the old drip-feed with earnings from a daily paper round. Rode it to and from school in Chichester in good weather (8 miles each way according to the Smiths speedo I fitted to the 26" front wheel - mine didn't have the dyno-hub), and on the early morning paper round in all weathers. Only parted with it when I moved to London to start my first proper job. Regretted it ever since!
Since arriving in Australia in 1976 I've owned a few modern bikes for pottering around on, currently riding a Papillionaire Classic, but haven't enjoyed any of them as much as that metallic red Palm Beach. Could be wrong, but I think the gents' model was in red, and the ladies' in blue (my mum bought one the year after I bought mine). Tend to see more of the ladies' blue models offered for sale in Gumtree and
ebay, some of them in good nick. I've been seriously looking on the 'net for the past couple of years and have never come across a good or even worth-restoring gents' version anywhere. That model - and vintage Triumph bikes in general - appear to be pretty well unknown here. I don't think there's any chance I'm going to find anything like it in Australia, so if anyone has or knows of a good one which might be for sale in the UK and you, Mad Doug, don't want it, I'd really love to hear of it.
I had been planning to visit the UK later this year and obviously that's out of the question now, but if the right bike came along I'd be prepared to pay a fair price and arrange for its shipping downunder.