When Liza and Josh told me their crazy plan, I did nothing; just [...].
I thought about glance, but I think glancing is more like looking briefly, rather than staring in bewilderment.
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If you are alternating, then you are not 'staring.'
In the context, the fact of looking at only one of the two at any point of time is of no significance.
As such, it should be fine to say "staring at them ."
However, if really needed, we could even say "looking alternately at them, utterly bewildered (or such)."