This is good advice for an apology for any important relationship. I particularly liked the suggestion to be specific about what you are apologizing for. Not saying "for anything I've ever said or done". I received an "apology" worded this way recently. It was NOT a sincere apology and I did not believe it for one second! Nice try. They were just words. Very disrespectful (and stupid) of you to think I'd fall for it.
"Too often we don't realize what we have until it's gone. Too often we're too stubborn to say, 'Sorry, I was wrong.' Too often it seems we hurt the ones closest to our hearts, and we let the most foolish things tear us apart." Unknown
pp Narcissists almost never apologize for anything they do. It's always someone else's fault. The only apology you'll ever hear is. .. "I'm sorry BUT. .." The 'I'm sorry but' is not an apology but a blame - shifter. When someone knows damn well they owe you an apology they become obsessed with discrediting you.