You will probably have to take the steering column apart to replace the switch itself. Switches cost less than $20 and are easy to find. When you've exposed the switch, it's mounted to the column with an internal lock. There's a hole in the side of the tumbler, and you'll have to poke in there with a drill bit (eighth inch, or a small punch) to push the mechanism and free the lock. On a Speedster, that's an easy enough job.
There are contacts on the back side that your wires are screwed into place on with brass keepers. Mark them before you take them off, and then put them back on the new one in the same order.
An important thing to remember on a VW-based car is the electrical system is backward, so disconnect the negative terminal on your battery before attempting to disconnect the ignition. You could disconnect both, depending on whether or not you have things wired in directly to the positive.
Get a voltmeter out and see if you have 12v at the coil. The distributor is on the negative side of the coil. When it's on, the ignition switch should run 12V from the positive terminal of the generator or alternator (whichever you have) to the battery.
It will also energize some of your fuses, which might explain why your lights still work, even though the switch is bad.
I'm assuming you don't hear a soft click-click-click?
To see how to do it, Muir's VW book is very handy. There's an exploded diagram of all this stuff, and he writes in a very easy-to-understand, kind of hippie way.
Good luck!
