That sign is part of the 6509 Westheimer shopping center.
As noted above, it was originally a scrolling text sign but went dead for years. I worked for a brokerage company that had sold the center to a New York group, (Izzy Ashkenazy), and some years later a billboard guy approached us wanting to revamp it as it was in a very prominent, (and grandfathered), location. While the city wouldn't allow any major alterations, they were allowed to "repair" it. So the billboard guy, the broker and two lawyers did a long term lease from the NY group and went looking for a tenant.
They found Select and instead of doing any kind of electronic upgrade, just fixed the spotlights and put up the plastic sign faces that are up now, (though they've been replaced a couple of times).
The billboard guy, (Jeff?), had numerous health issues and passed away many years ago. He was a good guy. I'm sure the long term lease is up by now.
Ashkenazy's son sold the center and is now a billionaire. Smart guy. He also sold the Page Parkes building at 2727 Kirby to Mike Atlas, as well as a few other things.
I always thought that sign had a lot of untapped potential as it is visible a long way down Westheimer from both directions.