Been thinking about this idea again, and...
One of the hardest things about being in a time loop, is not letting others know you're in a time loop. You might think this is a strange statement, but think about it. After enough times, after enough loops, you start to know things you shouldn't, some things become too predictable. What you know and shouldn't know can very easily become blurred lines after enough time has passed. This can be very dangerous to oneself if the wrong thing slips.
In a simple conversation, a detail that you shouldn't know may reveal itself without you realizing it. The other person, if they catch on, could very easily become suspicious of you. "How do you know such information, Did I ever tell you that, Were you looking/digging into me/my past?" That's what many would think, and it could lead to great risk for yourself, at least in the current loop.
But, what if we twist this, what if the person you're talking to knows of the time loop. Maybe you told them, maybe they have a way to believe you are in one, or maybe they don't and are just humoring you. What if, even then, you slip up, not just knowing something you shouldn't but that this isn't the first or second or even 10th time you might have had this conversation with them. Your responses, too quick, too automated, almost as if you knew every question but the last. Then you let on enough information, that an interaction like this occurs:
Gladii after meeting up with their good friend, began the "question answer game". One they have gone through too many times, but still want all the help they can get, even if its to go through all these questions again. After answering about 20 of the questions, with there still supposed to be many more to go, something changed as Gladii answers the most recent question, like a flicker in the friend's eyes. The flicker reflecting Gladii's very own opaque eyes.
"How many times?" their figure had turned suddenly very serious, and had begun stare daggers.
"...What?" Gladii asks, puzzling on how this conversation once somewhat normal now turned into an anomaly different from previous loops.
"How many times have you and I had this conversation?" Before Gladii has allowance to speak, the friend spoke again, this time their voice shaking slightly, "Gladii, how many loops have you gone through?"
Gladii goes silent, not knowing how best to respond to this changed game.
"Gladii, how many? 10? 20? 30? 100? 1000? How many times?" Their friend got more exasperated. Before they could continue Gladii opens their mouth to speak,
"Countless, I don't even bother trying to keep track anymore."
[End scene]
Idk, this is just a silly idea so far. Time loops are fickle things. Sometimes there are things that you aren't supposed to know in the current moment. Maybe, sometimes, those things, include what routes you have explored before.