Pizer is listed in Patrick Hanks’ American Dictionary of Family Names, with two provenances. As an English surname, it is a variant of Peyser, and and its etymology is available online. As a Jewish surname, its etymology is given as unknown. From online searches, I couldn’t even tell whether it was Ashkenazi or Sephardi.
So, I don’t know, and it looks like a lot of people don’t know either.