Time systems and zones are made up. Solar noon is spread over more than an hour in the central time zone. In western Texas, for example, solar noon today is at 2:07 while in Nashville it’s at 12:55. That’s pretty close without DST but in August it will be ~30 instead of 5 minutes off. Every time zone is like that except one specific longitude within the time zone.
Those parts of Texas now experiencing high noon close to 2:00 P.m… Are they on Mountain time or Central time?
I suspect they are erroneously on Central time and should switch to Mountain time…