When I try index({1,2,3},{3,4},"") returns {3,null} whereas index({1,2,3},{3,4},{}) returns {3,1}. Looks like when curly brace is put in default parameter, when there is no 4th index, it goes back to start and picks the first index. i don't think this behaviour is captured in documentation either.
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This happens with many functions mostly I this it is considering " " as string rather than considering as null what I think from perspective but it's quite funny how these function in the cases.