Just to be a bit of a prick here, but I'd just like to point out that your DM is running the golem so wrong it hurts.
An iron golem has no intelligence score (Unless awakened. Which, granted, is an outside possibility). No intelligence score means it cannot think. It cannot make assumptions, it cannot make leaps of intuition, and it cannot improvise. A golem can only do what it is expressly told to do. If the golem's instructions include "If you have to travel to any other floor of the tower in persuit of an intruder, return to your post via the stairwell once that intruder is dead or no longer within the confines of the tower." and you lure it to the ground floor and then stoneshape the stairwell away, leaving a open shaft where it once was, guess what the golem will do. It will stand there at the bottom of where the stairwell once was, because the condition "via the stairwell" can no longer be met, and its instructions did not include 'Jackie Channing' up a shaft that at the time of instruction did not exist. Now, if you went back down to the first level the golem would once again persue you, because that's something that's in its instructions. Intruders: kill or drive off. The golem's instructions couldn't even include "return to your post by whatever means necessary" because 'whatever means necessary' means nothing to the golem. It's totally incapable of thinking what measures would be necessary, on its own.
You can at best give a golem a list of If/Then statements that it will follow, and they must be explicit in nature, because again -no interpretation, -no improvisation. Personally, were I this golem's owner, I'd include two statements in its instructions:
1) If you cannot reach an intruder to Kill Them/Drive Them Off but are able to get within 10' or less, stand as close to the intruder as local conditions allow (moving toward the intruder until such movement is impeded) and repeatedly use your poison gas ability until such time that the intruder is Killed or Driven Off.
2) If you cannot reach an intruder to Kill Them/Drive Them Off and are not able to get within 10' or less, then proceed to the Alarm Gong located on the tower level that you currently occupy. If that Alarm Gong is missing proceed down one level and repeat previous instruction: move to current level's Alarm Gong. When an Alarm Gong is successfully reached, ring it until (Name of Other, Intelligent Guardian - maybe a bound outsider of some kind?) comes to you. When (Other Guardian) appears, obey their instructions until such time that you are instructed by them to return to your primary post and resume guarding.