Simple 43. doesn't require it.
Really, we have to rehash this again, Tom....
Generally, we have an option for maintenance entries, 1. a description (or 2. reference to data acceptable to the Administrator) of the work performed. (43.9)
There are exceptions.
Maintenance entrie requirements for inspections can be different than that, particularly if the aircraft is inspected under an inspection program... inspections and procedures for that particular program are followed [43.11(7)] which applies to parts 91, 125 and 135
The inspection program I work under requires the maintenance manual reference to be used whenever there is one for a specific task.
Ok, that all, only pertains to maintenance entries. It says nothing about what we are required to do.
So, we have 65.81(b) A mechanic may not exercise the privileges of his certificate and rating unless he understands the current instructions of the manufacturer, and the maintenance manuals, for the specific operation concerned.
And people admit they ignore the maintenance manual and do whatever they want and make a vague maintenance entry.