On opening my iPhone 5S for battery replacement, I managed to tear the Home button cable. ☹️ Of course, this led to need for replacing the Home button.
As the phone was already open, removing & replacing the home button was relatively quick. However, now TouchID no longer works.
I now know that in making TouchID secure, the screen, motherboard, and Home button are all uniquely identifiable, and tied together. Replacing any of them results in no more TouchID. Apparently the only way to maintain TouchID functionality is to have Apple perform any such replacement of the screen, motherboard, or Home button. Perhaps I can take the phone to an Apple store for help reintegrating things, but I'm not too hopeful there.