Would Jerry Brown have run for anything in his post-presidency?

[President Johnson]

Just few presidents returned to public service or ran for something after leaving the White House. How likely is it that Jerry Brown would have been one of these after being president? Let's say he would have won the nomination in 1992 and was in the Oval Office from 1993 to 2001. Does he still run for either California Attorney General in 2006 or Governor in 2010?

I'm asking because he didn't bother to run for Oakland mayor twice and then Attorney General after having been the highest ranking official of his homestate. Few former governors actually do that. So why not running for a position after the presidency?

[President Johnson]

Jerry Brown seems like one of those people who don't seem particularly interested or willing to retire for whatever reason.

He'd probably run for Governor in 2010 or for Senate to replace Boxer in 2016 (or both).

I wonder whether he'd lose his post-presidential privileges such as Secret Service protection then? And whether he'd still be referred to as "Mr. President." But this seems a fair statement.