As the bolded part says, you are only required to display your CHL if you have a gun with you at the time, even if it is not on your person. People without a CHL legally carrying in their cars have no duty to notify.Texas Government code § 411.205. DISPLAYING LICENSE; PENALTY.
(a) If a license holder is carrying a handgun on or about the license
holder's person when a magistrate or a peace officer demands that
the license holder display identification, the license holder shall
display both the license holder's driver's license or
identification certificate issued by the department and the license
holder's handgun license. A person who fails or refuses to display
the license and identification as required by this subsection is
subject to suspension of the person's license as provided by
Section 411.187.
That said, I would probably at least let the officer know I am issued a CHL to avoid any unpleasantness. I wouldn't necessarily hand over my CHL with my DL as I would if I were carrying.