You knew ahead of time you'd take grief for the somewhat tacky British/American comment....
I think it is intersting that American audiophiles seem to be obsessed with tone or tonal balance while British audiophiles are obsessed with PRAT. Both are essential to music. The below is just my take on the subject. I tried to read most of the posts but didn't get to everything so maybe some of this is repeated. Standard disclaimers apply -- YMMV etc.
As is indicated in the name PRAT, timing is essential. Actually, I think timing should be listed first in the acronym but TRAP just doesn't sound that great. One thing for sure, you can't have rhythm and pace without timing. ...
The audiophile term PRAT is an acronym coined by a Hi-Fi News reader to cover British reviewer Martin Collums' discussion of "pace, rhythm and timing". Since that time pages of posts are written attempting to explain it as a thing.
Given the option between an audiophile term and a music term, I'll usually take the music term*. Music supplies all that is required with its terms 'tempo' and 'rhythm'. No acronym is needed.
Tempo is the Italian word for "time" and is used in a way that refers to speed. How fast or slow a piece of music proceeds is a fundamental aspect of its character. There are at least 50 different tempo markings (instructions) used to describe the speed at which music is performed. And there is a time signature that tells us beats per minute.
Rhythm is a generic term that refers to any measured pattern in either sound or movement. In music it is the structuring of notes according to sounds and silences of different durations and the forming of sounds and silences into patterns. Patterns fit into a framework of beats. Rhythm is the essential element that makes music move.
Changing the tempo of music does not change its rhythm, it just speeds it up or slows it down.
* suggested reading: The NPR Classical Music Companion, ISBN 978-0544310933