The question is terribly confused, so let's unpack it.
With regards to the famous trolley problem, I know that
neuroscientists have largely found people believe it is morally wrong
to flip the switch to kill one man in order to save five strangers.
Well, you don't need to be a neuroscientist to find that-- a simple survey will do. But generally speaking, most people express moral qualms about throwing the switch, yes. So, this is either a sociological question (if you are quantitatively interested in people's responses) or a philosophical question (if you are attempting to analyze the ethical implications of the acts involved.) So far, so good.
I also know that they've found that the disgust centers in our brain
(such as the amygdala) light up on a functional MRI based on how
commissionary the act of sacrificing the one for the five is.
Here we've left philosophy behind, and moved to neuroscience. Neuroscientists have indeed found that the amgydala lights up on an fMRI when people think about disgusting things, and that the prospect of killing someone (as in the trolley scenario) is disgusting. Not a terribly surprising result, but there you go.
Now, we come to your question:
Thus, I am curious about the inverse: In which circumstances have they
found that people are actually more willing to to sacrifice?
What? You seem to be asking about a hypothetical situation in which people would be more willing to throw the switch (presumably,"more willing" meaning in this case "more willing than in the standard 'kill one to save five' scenario"). If that's what you are asking, the answer is trivial: if we alter the thought experiment to be 1000 people saved (or a million, or all of humanity) we find that increasing numbers of people are willing to throw the switch. Similarly, if we alter the experiment to be, instead of a person killed, a rat, or a watermelon, we'd find more people willing to throw the switch. Or, we can keep it a person, but change the result to be one of an injury instead of death. There are lots of ways we can rewrite the scenario to get different results.
But if that's what you're asking, what does neuroscience have to do with anything?
The way you framed the question seems to imply that neuroscientists have something relevant to say on the matter, but this is at odds with the content of the question.