Calum - best of luck in your quest for that '62 Bonneville. They are out there, you just have to keep beating the bushes until one emerges. And, speaking from experience,
try to find the cleanest example that you can. I have a '70 Bonneville which was a "rolling basket case" when I bought it. The rebuild/restoration process took the better part of ten years and it was a love/hate, on again/off again affair. It's easy to get sucked into rebuilding a vintage Triumph as it appears as though there are plenty of parts available. The only problem is that many of them are "pattern" parts, meaning that they were reproduced using measurements taken from an existing part - not an engineering drawing. So, a lot of times, the part "almost" fits and might need some "massaging" to get it to fit. You have to be part mechanic, part old world gunsmith and have a ton of patience. Working on a Japanese bike feels like a walk in the park, by comparison.
Again, good luck!
Mike
A pic of my vintage Bonneville. A '70 chassis with a later 5-speed '77 motor converted to right-side shift. 1940's manufacturing technology at it's finest!