Ash,
The problem with rebuilding a 350 (or a 500) Triumph twin in this condition is that the rebuild costs are nearly as high as the much more desirable 650's, but the end result isn't as valuable as the TR6/T120 650's. That's what an experienced old brit bike builder told me back in 2007 when I bought my first T120R as a wreck from the USA. He was spot on !
If you owned a Triumph 350 many years ago and hankered after another (to recapture your yoof), then fair enough, but otherwise it's just going to be a labour of love with little return, and probably zero profit. The low mileage doesn't mean much as it will still need a full engine rebuild after all these years, and that's £2K IMHO (more if you have to pay somebody to do it).
Another unfortunate consideration is that although it's a smaller engine than the 650's, the weight is still substantial because the frame and cycle parts are pretty similar to the 500/650's, so if you are getting on in years and are looking for a lighter bike than your Triumph/ BSA/ Norton etc 500/ 650's/ 750's, it won't actually make much difference.
For the money.....seeing as it needs a complete rebuild, it might make a nice Green Laner........invest a total of £5K and you wouldn't need to do much for the next few years, and it would provide a lot of fun. If it's really what you fancy, at that kind of money, then I'd buy it.......but TBH if you want a nice road bike without breaking the Bank at around £5K, there are much better bikes out there, as some recent sales on the Honda sohc Forum have shown.
