Also, left and right caliper may look the same, but they are not. I bought a left caliper thinking it would be a straight install.
Something must have been weird with your second caliper - there are no lefts or rights. They're all the same. I've never had an issue with a caliper not working on a particular side. Also, if they were handed, I'm sure they would have been stamped or some indication would have been placed on them.