This is a very interesting question, as I've also used the concept of equivalent safety for many years, but no, I don't recall an official definition anywhere. I just looked in my two favourite sources, the old JAR-1 and a book called "Initial Airworthiness" from Springer, neither have a definition either.
My understanding is that when compiling the compliance checklist against any of the civil design codes, you have to address every part, but you have essentially three answers you can give:-
(1) Irrelevance (e.g. the paragraph applies to retractable RATs, but the aircraft has none)
(2) Either demonstrated compliance, or a proposal requesting approval for a proposed means of demonstrating compliance.
(3) Equivalent safety: that the standard of safety provided by the method of evaluation shown, will be at least as great as that which would be provided by minimum compliance with the standard formally in place.
I shall watch this discussion with interest - although I wonder if you might get a better answer in Flight Test, where you're more likely to find people directly involved in aircraft certification, than here which tends to be more about operational safety issues.