I've hinted at this. Rather than asking what are the Gatekeepers duties, ask yourself what are the gates able to do?
"Hell's bells. The gates...they're...some kind of spiritual CAT scanner?"
"Among many other things," he said.
"But it's one of their function's, yes."
I would personally speculate that it is the instrument that allows movement between the various realms. That is also Mab's, and by extension, Rashid's eye in the sky. Sort of an all seeing eye.(I'm looking at you Doctor Strange) Oh and did I mention, branch predictor for the multiverse. Oh yes. And it also walks dogs.(Go RH)
Lame humor aside,
Rashid finding Harry near the Mothers cottage in Summer Knight.
Rashid magically knowing that Black Magic is afoot in Chicago.
Rashid watching the battle as it rolls towards the warehouse where Molly is to be executed, and stalling so the group gets to the warehouse first.
Rashid meeting Harry just off Demonreach, in Turncoat, where you get a tofer, the all seeing eye can see the link with Demonreach, and he states probabilities for Harry surviving the encounter.
From the Wiki
In "Love Hurts", Anastasia Luccio mentions to Harry Dresden that although the Wardens don't have orbital satellites for detecting dark magic, the Gatekeeper may know something about what's going on. She states that Rashid has a gift for sensing problem areas, but that no one has seen him for weeks, which is not unusual.
And bonus points.
Mab's snow scene of Marcone's take down in Small Favor.
And the Mothers crt eyes flickering as they find out about Harry learning the adversary's name in Cold Days.