is it really accurate to characterize the probabilistic assessment of a second engine failure as such failure being an utterly random event?
No, I don't think so; that's my point.
But the fundamental notion upon which the whole ETOPS rule is based is that if one engine fails, the probability of the second failing before the aircraft can land is no greater than it would have been without the failure of the first engine to fail.
In other words; if it does fail, it can only do so for a reason unconnected with the failure of the first engine to fail, so that such an event is entirely random. I don't buy this, and nor, I suspect, do you.