But there are even greater differences for Time Patrol agents. Some of the experiences that they remember did not happen, at least not in the current timeline, and some of the events that they investigate may have causes that are also not in the current timeline.
"You didn't age in the Patrol and you never got sick..."
-SM Stirling, "A Slip In Time" IN Multiverse, p. 73.
Not aging, you would lose any sense of personal duration. Some remembered experiences would be longer ago than others but you would not have aged in any way since experiencing them. Remembering an experience from decades ago, I reflect on how young I was then but this sense of increasing age would no longer exist. And it sounds as if Patrol agents do not retire but continue working indefinitely. Their careers have not a finite duration with an end point but a sort of timeless present.
"Maybe returning to New York on the day after he left it had been a mistake."
-Poul Anderson, The Shield Of Time, p. 3.
Imagine being able to spend weeks in Tyre but then return to New York on the day after you left it - and also being able to control exactly how much time had elapsed between departure and return. Surely time itself would begin to seem unreal?
A Patrol agent would be able to strand an enemy, say a Neldorian, in the remote past, not think about him for say five decades, then:
decide to leave the Neldorian back in the past or
retrieve him from the moment when he had been deposited in the past or
check on his progress five decades after he had been left in the past or
check on his progress at any point between zero and five decades.
It is as if the Neldorian is frozen in the past. He is not but that is how it would seem. Again, would Patrollers be able to retain any sense of time as a reality? They know that they will die some day but not of old age so they have no idea of how near their deaths may be. Their lives just continue, although not in a linear chronological sequence, until they stop.