Here, we'll discuss when Traitors will most likely want to take someone out, how they make the decision to, and what makes a good target. This should also work as a helpful resource when trying to adopt the mindset of a Traitor during an investigation.
Despite Benoit Blanc's disdain for Cluedo, the average TTT player will rely on means, motive, and opportunity as a basis for their crafting a version of events to rely on.
As a Traitor, you'll always have motive in the form of needing to kill people to win the game, so we're more concerned with the means and opportunity part.
Drawing first blood in TTT ideally happens quickly and quietly for the Traitor team.
With everyone spawning sparsely around the map, Traitors are effectively given a golden opportunity to reduce the Innocent team from the start. This first kill, while it can be frustrating for the victim, energises the game; it gives the Traitor team confidence to go about their business, the Detective roles something to investigate, and the other players something to fear.
With the way the gamemode is designed to work, this is often impossible to do in good time but, with smaller maps, it can happen. This strategy does, however, have a host of unique issues associated with it.
All that the Traitor team need to do, when met with this outcome, is focus on weapons or Traitor shop items that can accomodate it; taking advantage of the shotgun's effectiveness, or using a SLAM/C4 can very easily clear a small space even by accident.
Not to mention, if you're not typically taking the first shot (which Innocents tend not to do for fear of killing a fellow Innocent, or Jester), having more space to have to traverse between you and a Traitor means less accuracy for them when they try to shoot at you as you go about your business and frustrate them by being so inaccessible.
With the first kill of the round being the easiest to premeditate, at a time where the Innocent team is least on-edge, and to have the opportunity handed to you on a silver platter, it is safe to say that this is the easiest one to both perform, and get away with.
If a lobby full of people hear a 'random shotgun blast' a great distance away, they will assume some, or all, of several things:
Which, to be fair, these are all perfectly valid reasons.
As such, the first death in an average TTT round will only be discovered later, as a body. If you aren't directly beside the murder as it happens you will typically try to avoid adding to the body count; if two people went to investigate, for example, they might assume the other is a Traitor by default (and then you just get another dead person, and an injured trigger-happy Innocent with a kill count).
All of this to say, the first death in the average TTT round will leave a body to be discovered later, and only then will questions be raised.
The tension is on, now. Both the Traitor and Innocent teams have things to be afraid of, Traitors have to fear that they'll be discovered and investigated well, the Innocents have to worry that they'll turn on each other by mistake, or be taken out by the Traitor team.
Bear in mind, even items that destroy bodies like the 'Flare Gun' won't remove all of the pertinent evidence from a crime scene (bloodstains, scorch marks, etc.). Once you pull the trigger on that first kill, you're agreeing to manage the consequences.
Every kill that follows the first, or the first discovered kill, will be harder to get away with. People will be more on edge, they will share the evidence involved, they will know which players they were with when the kills took place, and band together with them.
Splitting players apart and picking them off will only get more challenging as de facto factionalism takes hold. The best you can hope for is to play around the objectives decided by the Detective, or to try and pre-empt which objectives will be set by the Detective, and to prepare for them to go wrong when they take place; if you assume that the current Detective will want to make use of a Traitor Tester (if the map has one), you want to get there first and set up traps, or ensure you're ready to react if a less-than-desirable result happens.
Using Traitor Buttons, during this stage of the game, is great, too. These are tools added to each map by the map's creator; they might be 'blow this thing up' triggers that you can press as someone goes past a significant object, or so on. Knowing these requires map knowledge and careful timing, however. And it also arouses a lot of suspicion if you stare directly at it, as it happens, as you'd need to do so to press 'E' on the button in question, marking you with immense suspicion.
As the Traitor team kills more people, they will be afforded more credits to buy esoteric equipment to help them keep their streak going, this is the best advantage they have in an otherwise fair fight, and identifies them as a Traitor immediately when they start to use that equipment, or hold it out openly.
Killing the Detective makes the Innocent team less organised, gives them more credits than an Innocent kill, and mitigates the effectiveness of a Detective shop existing, so the Detective is almost always a, if not the, priority target.
Players that are clear of suspicion, or seem effective, are the most common or necessary targets. Opportunity/convenience of killing someone often trumps this rule.
The game gets quiet.
As Traitors near victory, the player count is whittled down, they'll often be talking most to try and steer the direction of the game, to entice people to talk, to share their locations and to cover up the awful quiet that the voices of countless victims once filled.
The foxes are chittering at the doors of the coop, now. All that remains, once you've got a feel for the gamemode, is defend yourself as best you can.
It can be a valid strategy, for both Traitors and Innocents, to talk less, so people can't be sure which players are alive.
Typically, when just two or three people are left, everyone is a 'kill-on-sight' target. The game will end, one way or another.
But it isn't always this tense, because if an Innocent just isn't paying any attention at all, they might assume people just got quiet for no reason, and walk into a Traitor asking "Hey, where is everyone?" before a comically large shotgun blast inverts their facial structure.