This is the pythonPython script I wrote to accomplish the task. The code throws multiple errors.
This code is based off of code posted by a previous user in response to a previous question that I asked on this issue that was placed on HOLD. The code the user kindly provided did not throw errors but it did not produce the desired result; it generated random points in the full feature class (all zip codes in the state) extent not in the extent of a given individual zip code. Here is that code: