I finally broke down and googled the question and found a ton of stuff on this issue. Here's an (non-copyrighted) excerpt from one of the more concise discussions -

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As of September 1, 2011, most Texas employers cannot prohibit employees from possessing guns in their locked, personal vehicles on employers’ premises. Texas Senate Bill 321 (“SB 321”) – which Governor Rick Perry signed into law on June 17, 2011, and which goes into effect on September 1, 2011 – restricts public and private employers from prohibiting an employee who holds a concealed handgun license or “who otherwise lawfully possesses a firearm, or who lawfully possesses ammunition” from transporting or storing firearms or ammunition in a locked, privately owned motor vehicle located in a parking lot, parking garage or other parking area the employer provides for the employee. There are exceptions to this prohibition:

Employees still cannot possess firearms in locations prohibited by state or federal law (e.g., Texas Penal Code § 46.03 prohibits individuals from possessing firearms on school premises, secured areas of airports, polling places, and other locations);
The prohibition does not apply to: (a) school districts; (b) open-enrollment charter schools;
(c) private schools;....

Haynes and Boone, LLP | Newsroom | Texas Employees Receive New Gun Rights

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It looks to me like, since premises does not include school parking lots for CHL holders, a school district could not prohibit a CHL holder from locking their handgun in their car parked on school property, but they can prohibit them for employees since this new law does not apply to school districts. Where do we find the geniuses who write this stuff?