Each player would have 20 minutes, each player is contributing to their own pooled timer. It's not a single timer where both players are contributing to reducing the same one rofl.
Okay since turns are simultaneous I was thinking the pool would be shared. So your turn clock would stop when you hit end turn with no relation to when the next turn actually begins (if you ended first) and the one who uses their pool first looses. If that is the case then 20 minutes is not the maximum a game could last as you said because who is taking longer could alternate radically with the extreme being one person immediately hitting and and one person taking the full time for an almost 40 minute game. Also if you end turn and then undo it to change things is the time that your turn was ended retroactively taken out of your supply since you were using it to think things through? I can only see two scenarios here, one where the pool is shared based on how long the turn takes (turn in this case being from last turns end to this turn ending which is decided by the slowest player) which is highly exploitable. The other scenario goes into very murky territory with a max game time that is still highly variable and players betting and rationing time in long games (If I end turn now I can plan without losing my pool so long as I un-end it before they finish). I am in favor of the turn timer being capped at two minutes but, simultaneous turns make an overall pool of time just seems like a somewhat confusing and occasionally even stressful solution to a problem I just don't have. I could see it be necessary in tournament play or as an option for casual play I just don't like it as the standard.
I guess there is a third option of whoever has taken the most time at the end of 20 minutes looses. That still seems inelegant and outside of tournaments unnecessary and also still leaves open the question of ending and unending turns. Also how does the resolve phase factor in? I don't know how it currently works with turn timers as is but does looking at the results of last turn take time out of your current turn? If it does that seems pretty noob unfriendly as it disincentives them seeing how things resolved and encourages them clicking through without looking. If it doesn't then you are giving the players an amount of time out of the system making this their new planning phase.
Since turns are simultaneous, it's 20 minutes maximum. Players have their own pool which deplete at the same time but stop at the time their turns end.
Turn 1 - Player A takes 30 seconds, Player B takes 60 seconds.
Player A's remaining time 19:30; Player B's remaining time 19:00
Turn 2 - Player A takes 15 seconds, Player B takes 60 seconds.
Player A's remaining time 19:15; Player B's remaining time 18:00
I never pointed out what should happen if a player runs out of time. When a player's pool runs out completely, the player could be subject to a different type of penalty, such as 15 second forced turns instead of outright losing.