The user had a two-fold issue with their Business Rule (BR) not firing:
The causes were as follows:
In each scenario, the customer was counseled to adjust their BR to align with their process. For example, ensure that any technician inserting a record manually via the Platform UI needs to do this X way, and whenever an integration inserts a record per the code it is sending into the ServiceNow instance, that code needs to be consistently formatted in Y way to faithfully trigger the BR.
When these adjustments were made, the behavior resolved in both scenarios.