I've been "between jobs" many times, and heard that phrase "over-qualified" many more times. It seems like a real slap when you're having trouble paying the rent and you're there, willing to be their HTML-boy for a regular paycheck.
To be an SEO, you should understand how all the engines work, what gets a site into the top ranks, and be able to implement practical strategies to push a site up the ranks.
An SEO is often a site "doctor". Your role is to diagnose problems and be able to recommend solutions.
Understand how indexes work, spiders and robots and what to do if your site is double-indexed. Learn how to find out if pages are duped. Learn about canonical URLs and URL rewriting. Be able to load a page and see what HTTP headers are being exchanged. Understand the difference between a 301, 404, 302, 200, 501.
The best SEOs I know have hundreds of sites at their disposal, where they try odd things and do experiments to see first-hand what works and what doesn't.
One SEO once told me, "You won't really know what it takes to get banned from Google until you try to get banned from Google. Then you know, and you can walk right up to the line without stepping over it. That line is where the #1 sites sit, and that line keeps moving." -- That's advice I'm never going to forget.