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I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space.
This source provides a nice explanation of the Wick rotation procedure for fermions in 4d. However it leaves the odd dimensional case as an open question.
$\begingroup$Perhaps one method would be to perform the Wick rotation in 4d and then compactify a spatial direction to a get an (effective) 3d result. One might be able to generalise to higher odd dimensions by compactifying 6d, 8d, etc... in a similar manner.$\endgroup$