What's the etiquette for resigning when your opponent is having difficulties?

I've had a couple of times when my opponent has been in a clearly winning position, but has disconnected. This is sort of annoying because from my point of view I've got to wait 5 minutes for the system to auto-resign them, and it's not really fair on them either, because they basically won, but then had an internet connectivity problem. Is it best to resign in their absence? A variation on this is when someone's done something which is totally obviously not what any sane person would do. I've had a couple of occasions where the touch-pad on my computer has led me astray and done something spontaneous, and  I've found I moved a piece I didn't intend to touch, to a place I'd never move it. I assume my opponent has done something similar; it's a touch-pad shirt-cuff accident! I usually offer a draw when this happens. But what's the right thing to do?

@1

"my opponent has been in a clearly winning position, but has disconnected"
++ If you did not resign before he disconnected, then why resign after and because he disconnects? You clearly had some hope, how did that hope vanish by him disconnecting?

"when someone's done something which is totally obviously not what any sane person would do" ++ So if your opponent hangs his queen, you offer a draw?

You should not hand out half or full points for your opponent's problems with his connection or mouse.

a win by disconnect is like winning on time in a losing position, winning due to a mouse slip or winning from a brain fart blunder. it doesn't feel like an actual win but it wasn't my fault and i will take the win.

Sometimes I play on, in a basically lost position, because I think the opponent has a right to see it to the end! And yes, sometimes if someone hangs a queen, I offer a draw, because it seems to me to be an unrepresentative end of a game! But hey, maybe I'm weird! I suppose you're right, really; for those who want to play seriously, it's a good idea to get out of the habit of hanging queens.

I have wondered about offering a take-back for an obvious mouse slip. Something like "I'll play a do-nothing move, you undo your move, I'll undo mine, then you can play the move you intended " Of course this might not be possible if the mouse slip was with a pawn or involves a check, and it does require a lot of chatting to explain, which might be a problem if the players are low on time or don't have a language in common. Does anyone know if an offer like this would violate fair play policy, since it is effectively collusion?

I feel stupid when I see you guys like come on! It's online rating nobody gives a damn about it. It's not your fault after all.

The slips also come with it. Today is you tomorrow your opponent, I accept it as a part of the sport, equally to all.

About the etiquette. I had a game where at the end I was in certain losing position. I think I had couple pawns and king. Pawns I couldn't promote anymore and opponent had rooks or rook and queen and pawns to promote. So when I resigned the opponent said "Coward" in the chat . It was quite funny. I guess he got mad when he didn't get to finish the game with mate.