Gaus
The only way to escape the prison was to study it.
Gaus sat on his bed with his legs crossed, thinking the recent events over. Of the four things he discussed with Rachel that could trigger the time loop, Gaus chose the first one - Rewind. Rewind should be the cause because only then could Rewind copy (save) what happened. In other words, if the twenty-four-hour loop wasn't caused by the Rewind, then Gaus wouldn't be receiving 'magiwatch has saved 24 hours' every day.
The question here was: which rewind was causing the time loop? Was it his, or the marines', or was it an entirely different Rewind, a third one? After much deliberation, he decided there was another Rewind besides his and the marines'. He just recently came into the loop, so it obviously couldn't be him. And The Master had been in the loop before the marines, so it couldn't be them either since the loop had been around long before them. Which left the possibility of a third Rewind.