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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I believe this has been brought up before - I'm never clear on why this happens, but index() does some... funny(?) things in the background when given corner cases, so at this point I think this is sorta-expected behavior.