'been reading the thread with interest. Not being a twin driver, but a single, every failure is an automatic emergency. And you know what, I think that's actually very easy. Let me explain.
The posts I have read so far have all centered around what the outside world is going to do when they hear your mayday or pan call. Will ATC clear the airways for you or not, will the fire brigade come out of the shed in full force, will everybody else shut up and look out for you. That's all very fine and dandy, but there's one other thing that a mayday call will achieve.
And that is to convince yourself that you have an emergency.
We've all heard the phrase "the second engine just takes you to the scene of the accident". There's also a lot of other stories, non-aviation related, of people who got into trouble in arctic or desert condition and despite the setbacks/loss of all drinking water/malfunctioning of critical equipment/whatever, decided to carry on with the original plan. Or rather, did not decide for themselves to treat their situation as an emergency, kept on doing things towards achieving the original goal and died trying. If they would have declared themselves in an emergency (even if they had no means of telling anybody else) and then acted upon that declaration - meaning from that point on the only priority is survival - they would have lived.
One example. There's a movie about a couple with a young child who had to cross the Rocky Mountains (I think) in inclement weather. All passes were closed, except for one, they thought. They missed a "road closed" sign, got stuck in a snowdrift, car could not get out etc. Instead of the guy walking five or so miles *back* to civilization, he continued for I don't know how many miles forward, over the snowed-in pass, on foot. Spent a couple of days bunched up in a hole somewhere, several fingers and toes frozen off. I don't recall the movie exactly, but I do recall that civilization was only about five miles back down the road. If they would just have talked between themselves, came to an understanding that it was an emergency, assessed their situation, abandoned the original plan (which was to get over the mountains), and looked at what other options were available and sensible, I doubt whether the situation would have warranted the making of a movie.
So declaring an emergency has a very important psychological aspect. And that's that from that point on, your survival is the most important consideration. Saving the airplane is secondary. Exorbitant landing fees and a lot of paperwork because you landed at Heathrow without proper clearance and handing arranged - don't worry about it. Reaching your original destination - who cares. As long as you can walk away from the situation.
And as I said, if the donkey stops in a single, the decision to declare a mayday is easy. The hardest decisions are when the situation is not so clear cut. And in such a situation, if you do declare a mayday anyway, to me it means you've made your mind up. You are going to treat the situation as an emergency and make survival your first priority.