TV Out on the iPod Classic requires an Apple Universal Dock in conjunction with either the composite or component leads mentioned above. I understand an SVHS to SVHS lead will also work in conjuction with the Apple Universal Dock.
I have a dock from a 4G iPod photo, which predates the Apple Universal Dock. Apparently it lacks an Apple authentication chip (as do many third party docks), and so cannot be used for video output on a Classic, regardless of the lead used. So if I want video out, I have to buy a brand new Apple Universal Dock!
Neither does
this lead work with the Classic - video can no longer be output via the headphone jack.
It is rumoured this change has been forced on Apple, as the Classic can support output at 480p which could be used for producing good quality copies.
As mentioned, you'll also need the 1.0.2 firmware which lets you select video out as on/off/ask.