Asklemmy

There's a reason so many poker players wear sunglasses.

Anyway, try to preempt your emotional reaction. There's always many different flavors of reactions we can have to something really negative, which normally depends heavily on mood. By default, this all just runs unconsciously, but it doesn't have to. Of the many potential options, like anger, sadness, condescending disdain, arrogant bemusement or surprise, you can try to consciously pick one and channel your feelings towards it instead of just letting your feelings run wild.

Or you can just practice a proper poker face, but that can be really hard. Doable though, just takes a lot of practice. Playing poker would be an effective way to get that practice.

I've heard of an acting game where one will sit with a straight face and everyone else tries to make them laugh.

Maybe find videos that trigger the emotion you wish to suppress and watch until you have no visible reaction?

Not specifically for the eyes or posture, but for overall approach and attitude to situations like this:

• Marcus Aurelius' quote: Begin each day by telling yourself: Today I shall be meeting with interference, ingratitude, insolence, disloyalty, ill-will, and selfishness – all of them due to the offenders’ ignorance of what is good or evil. - and stoicism in general.
• Imagine them sitting on the toilet. You can't take them too seriously like that.
• Take a longer perspective: consider whether this interaction will be of any significance at all in 10 years time?