Not sure how the actual process works for CHL from the DPS side of things. Both me and the wife (AKA "she who must be obeyed) went through the process, I took the CHL class with the wife even though as a Honorably Discharged vet it wasn't a requirement. I'm glad I did; I learned a lot about the laws, especially as they pertained to where CC is allowed and where it isn't allowed. I also learned when force can be applied, especially the significance of deadly force. Serious stuff and I pray the occasion never arises.
So, I know that our credit cards were charged by DPS on 11/24/2014. Does that mean the process started then? I do not know. What is actually involved, what does the State do? I reckon they do a background check, both State and Federal. For myself I imagine they also look at my military background. I was a member of the Personnel Reliability Program in the USN, my thoughts is 'that is a good thing' since in effect I already have been vetted. Of course that was many years ago, not sure it matters....other than only having to pay $25.00 instead of $140.00!
Is the wait time a standard time-frame for people with no background issues? Does the time of year matter? I'm guessing this is a busy time of year. It's the Holiday season which means the DPS has people taking time off, there are probably lots of folk trying to get CHL before Christmas.
What is a "typical" wait time for electronically-submitted applications?
How are we notified of a "change in status"? Are we notified via email? Is calling in the only way to find out? I haven't been able to find anywhere to log in to the DPS website and check the status, that would be the simplest way.
Of course, there's no real rush, it will come when it comes....but I also feel like a kid who's sent in his cereal boxtops and is waiting for his toy to arrive in the mail!

Well, there's my $0.02 Remember: Stay safe, and JOIN THE NRA, National Association for Gun Rights and Texas Concealed Handgun Association!! Defend your Right to defend YOURSELF!!!