Kind of like the PCH, the Tail of the Dragon (ToD) is a bucket list thing for a car guy - and like the PCH, I wish I had been able to do it before it was hugely popular.
As others have said, it's unbelievably crowded, very heavily patrolled, and a LOT slower than I imagine it was before it became famous. It's an amazing stretch of road, and I can only dream of what it must have been like before packs of accountants on Harleys, RVs, leaf-peepers, and the occasional delivery van all decided it was a destination to be taken in at 3/10s speed. Fast cars or bikes who came a long way to drive an iconic road get behind all that, get frustrated, and do stupid things.
It's super-cool to have the images the photogs stationed on the corners shooting thousands of frames a day can provide for short money (I've got two of them blown up to nearly billboard size in my shop), but it's kinda' like Disney World - I feel like the idea of it exceeds the reality at this point in history. It's just too popular.
That being said, I've got a ToD sticker on my windshield, and a shot I took on the PCH as my phone background, so there's that. You've got to do it once or twice - but having done it I can tell you that there are many, many roads not overly crowded and not overpatrolled in the same area.
"The Rattler" is that kind of road - it's longer, faster, and 10x more fun.