It’s the part where they’ve been trained in a style.
Look, I would like to be able to say that a trained fighter is less likely to participate in a violent action simply to prove their own strength, but I’ve known a few who trained precisely for that purpose. I’d also like to say that a trained fighter will be more capable or risk assessment than an untrained fighter, but I’ve known too many martial artists for whom that is completely untrue. In fact, the fact that they had training made it more likely to be hurt because they made stupid decisions in a bad situation.
Here’s the thing, nothing is universal. There are exceptions to every rule and the rules like life often change with a person’s background, life experience, and based on what they know. The best way to indicate that your character has training without explicitly having to say it, is to pick the style you want them to know, or simply begin going through several different styles, particularly the philosophy behind them and start generating an appropriate outlook. A character is defined by how they see the world, think about that world, and how they behave in it. What they have been trained to do will distinguish what they see. For example, what an assassin will observe first about their environment will be different from the what a thief or spy do, a cop and a soldier may notice similar but different things about a situation. Once you have established what kind of martial training (and subsequent observational skills) you want your character to have (or they need for the story to work), you’ll have a much easier time pinning down their character and finding a place where you can begin your research.
How To books, memoirs, etc, are excellent beginning points. If you live in a place where there’s a close library, you can always ask a librarian at your local library to help you. Start reading more books by authors you admire (and even the ones you don’t) with characters similar to the kind you’re trying to write.
This will be difficult, because you’re also going to have to learn how to do those things or at least the business of pretending to do them. Learning how to see the world from a different perspective, like playing the “What Can I Use As A Weapon” game at local businesses or making observations about people in a crowded area, will all be helpful to your being able to imagine different scenarios.
I personally always start with character roles for precisely that reason, if I don’t, I’ll get into the centipede dilemma and get stuck. When it comes to a cheat sheet, that’s where I can’t help you because for every example I can come up with, I also find a counter example from my own experience or remember a style that doesn’t fit the criteria.
Instead of focusing on what everyone does, focus on what a certain subset do. By limiting your focus, you can generate more information. If your character came from a warrior culture, research different warrior cultures to find one that will fit your setting. If your character has a backstory similar to that of law enforcement, research that.
Ask yourself some simple questions:
If my character was in a grocery store what is the first thing they’d grab to defend themselves? (Don’t look for the best thing, look for the first)
What does my character look for when they’re in a crowded place? What do they do? Are they comfortable?
When my character meets someone new, what’s the first thing they notice about them?
If someone points a gun (or time period appropriate weapon) at my character how do they react?
If someone points a gun (or time period appropriate weapon) at my character’s family how do they react?
If someone points a gun (time period etc) at my character’s friends how do they react?
If someone points a gun (time period etc) at a complete stranger in my character’s vicinity, how do they react?
Every character is different, by working backwards from their reactions to different situations, you’ll find the best way to communicate to the reader that they know what they’re doing without them ever having to tell it straight out. But, you’ll need to research and experiment with that on your own. I know it’s frustrating to hear: get to know you’re character. When your at the beginning and in a hurry, it doesn’t feel like an answer.
I have faith that once you narrow down your focus, you’ll figure it out. Sometimes, the smallest details are the answer you need.