I recall once reading in a 4th Ed book, rules for having magickal items with Scores in different Abilities. The Example from the book was something to do with a statue being taught to play music. My question is thus;
Which book, what are the rules specifically, and can they be used in 5th Ed?
It can be done for Automata, assuming you have been initiated in that mystery (it's a major Verditius mystery, but has somewhat spread outside the House). See Houses of Hermes: Mystery Cults pages 128-131.
Is the ability rules actually part of the mystery, though? I mean, do you have to be initiated into the Mystery to put an ability into a non-automaton?
Well, that's one of the few things (along with their inherent Magic Might) that seem to make automata at all desirable, so I don't think that, initiated or not, you would be able to put abilities in non-automata. Without it, automata would merely be unusually expensive, complex and fragile greater devices.