Yeah, learn the scripting language of the tool you use (I think MaxScript or MEL would be most useful to learn - they'd be the most desireable in the industry). Pick a problem and see if you can script a solution to it. Or a new feature for a tool. Or just adding functionality that you think would be useful.
I'm not sure you need to know C, that'd likely be more focused towards Tools Programmer (writing level editors and game engine tools). It still might be useful to mess around with - especially if you plan on writing plugins as well as scripts.
Learning UE3's material editor for materials and screen shaders would also be a good move.
As for what Tech Artists do... it's a pretty big range of stuff and the details can vary from place to place. But overall they write tools/scripts for the artists to speed up the workflow or bridge gaps in the pipeline. Tech-heavy or complex particle/shader effects and tools to control them.
The site mathes and Glynn linked to should give you a much better idea of what's required - some good stuff there
