broken hub dynamo lights 80s Triumph
Basic troubleshooting steps

1) Is there power coming from the dynohub?  Use a multimeter on AC 6V (possibly 20Volt setting required on a standard meter)

2) Is the power capable of flowing to the lamps?  Use a meter on continuity-beep or on resistance setting to check.

3) Does the lamp fitting carry power to the lamp?  Same as #2

4) Does the lamp work?  Use continuity or resistance test again.

Replacing the wire is a good idea if it looks manky, and new lamp holders will give you more light for the same input.  The hub is the most expensive part.