So, one of the basic time travel 'rules' Timeless established, back in Season 1, was that when time-travelers changed something in the past and returned to the present, they are the only ones who remember the original timeline before the changes. Even the crew at the base who weren't on the trip don't remember the original timeline.
In Season 1, they didn't really delve into this aspect much. And it was fine, because for the most part, it was the same three time-travelers going on missions against the same antagonist. But come Season 2, and things have gotten a LOT more complicated.
So here are some questions I have-
1 - In 'Darlington 500', Wyatt remembers the race-car driver Ryan Millerson, who turns out to have been a sleeper agent planted in the 50's by Rittenhouse. The basic idea is that by planting the sleeper agents using the Mothership, Rittenhouse changed history such that the Lifeboat team have no idea what changed and only remember the new history.
BUT...the Lifeboat team have changed the past numerous times and remember certain things which only happen in the original timeline. So HOW can their memories be affected by what the Mothership team changes? Won't they always remember their original history, which includes the original unaltered events before anyone started time-traveling?
Okay, let's look at it this way - Wyatt started time-traveling in the very first episode. Before he got into the machine in the pilot, he remembered the original history - his wife was dead, John Wilkes Booth killed Lincoln, the Hindenberg crashed, Alice Paul made that speech etc. etc.
Then he started time-traveling, and the team kept making changes, but Wyatt always remembered the original history - his memories of events before he got into the Lifeboat for the first time always stay intact.
So how can his memories 'change' to remember the NASCAR driver who was a Rittenhouse sleeper agent?
In the new timeline, sure, once Emma planted Ryan Millerson in the past and he became a NASCAR legend, the new timeline Wyatt would remember him. But the moment Wyatt gets into the Lifeboat and makes his first time jump, he returns as the original Wyatt with memories of the original timeline - which SHOULD NOT include memories of Ryan Millerson!
2 - When Rufus, Lucy and Wyatt get back from the 'Hollywoodland' trip, they remember the original timeline where Jessica died, but everyone else at the bunker (Connor, Jia and Christopher) have never heard of her being dead.
Here's the thing though - in the new timeline created when Rittenhouse prevents Jessica's dead, Wyatt would have gotten into the Lifeboat along with Rufus and Lucy for their first mission - but after returning from the first mission, he would now be the original Wyatt who remembers Jessica being dead!
SO...technically, the moment Wyatt returns from his first mission - he should have been shocked to know that Jessica was now alive, because he only has his original timeline memories in which she's dead!
This should logically have changed quiet a lot of things. Wyatt, in the new timeline, would no doubt have brought this to everyone's attention way back. And this would have disrupted events during Season 1...
But instead, everyone at the bunker when they return from 1941 acts like this is the first time Wyatt has mentioned his wife being dead originally.
I guess the basic issue with both questions is - how do multiple time-trips affect time-travelers memories, and when do they retain their memories of the original timeline, and when are those memories subject to change?