Geshem was not mentioned when his fellow adversaries Sanballat and Tobiah were mentioned in Nehemiah 2:10. Perhaps that is because he was further removed from Jerusalem than his two peers. We know from sources outside the Bible that he governed a district of land south and east of Jerusalem (much of which was/is wilderness). Theoretically, this area was under Persian control, but in fact Geshem could largely reign quite independently from the Persians.
19 But when Sanballat the Horonite and Tobiah the Ammonite servant and Geshem the Arab heard of it, they jeered at us and despised us and said, “What is this thing that you are doing? Are you rebelling against the king?”