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I'm sure many of you know about Dolby Atmos. It supports typical surround sound, with the addition of speakers intended to be placed up high, near the ceiling. I've seen it this type of surround sound described as 7.1.2 or 7.1.4, meaning 7 surround speakers, 1 subwoofer, and 2 or 4 ceiling speakers.

I was curious to know, does the codec state how many discrete height channels exist for the ceiling or can that be determined?

I'm ripping Teenage Mutant Ninja Turtles (2014) and it uses Dolby Atmos 7.1, but I'm curious to know if it's 7.1.2 or 7.1.4...

Atmos doesn't work like that, it doesn't have "discrete" channels in the traditional sense.
Simplified: Atmos is object-based audio, which means it has explicit audio for various audio sources placed in a 3D space, and the Atmos receiver is then responsible to map those to discrete channels according to which speakers you have placed in your room.