before anything else, i think it's important to lay out the general framework for optimal MGE matches. arena-specific advice can only follow by knowing the matchup & the type of fight in play.
each fight of an MGE set should be strategically categorized in one of three ways:
1) the first fight -- determine the nash equilibrium (which is usually, but not always, the center of the arena based on your spawn relative to your opponent's) and then immediately begin the fight from said position, readjusting view angle & character placement based on your (im)precision & your opponent's (im)precision (i.e. damage dealt/received and, more importantly, expected damage to deal/receive). this ideology is the most straight-forward for scout vs scout, but it holds true for nearly every single matchup save for possibly demo vs any class, as demo usually performs better the farther back he can hold. it can be tricky to determine the nash equilibrium for scout vs soldier as either role, but the best advice i can give is to not underestimate having low ground as a soldier if you have prior knowledge that the scout is clumsy or tends to play imbalanced (usually in the forms of playing extremely widely or double-jumping very naively). on the flip-side, it's important for scouts to constantly attempt to get a view-angle advantage over their opponents unless they have a reactionary &/or predictive advantage over their opponent (the element of surprise).
the other two categories are very match-up & arena -oriented, but the most important mentality to have across both is to think about influencing your opponent in the long-term so you can better predict what he's going to do in future matches. going onward as generally as possible...
2) won the last fight -- establish and maintain momentum by identifying view-angle discrepancies between spawns (e.g. you're playing scout and the soldier spawns perpendicular to you looking at the center of the arena whereas you're looking right at him). utilize your first-shot speed advantage (but be wary of having less ammo than your opponent on respawn if you used a hitscan weapon to kill your opponent in the last match) and plan to close distance.
3) lost the last fight -- utilize your greater ammo count if you have a hitscan weapon &/or re-angle your opponent as uncomfortably as possible to break momentum. this is the most physical of all the fights, but prediction is still a major factor. for instance, if you're playing scout & your opponent tends to have a passive-range of movement, approach it like a spy & jump/double-jump behind him to flip the view-angle discrepancy in your favor. at the same time, if your opponent overly predicts hyper-angular play, punish with a tight-aggressive playstyle by moving slightly diagonally into said opponent. always play around with depth-perception: move backwards to amplify angular discrepancies and then follow-up by squeezing in between shots to maximize damage dealt & minimize (but not necessarily negate) damage received. mobility is extremely important to factor when reestablishing momentum; sloppy movement can exhaust you & waste your efforts in otherwise close fights. most importantly, realize that it's completely normal to lose multiple fights in a row in MGE. momentum can be very hard to overcome, with ammomod arguably being the hardest arena when said momentum is against you.
playing into view-angle discrepancies & deceiving your opponent, you don't necessarily have to stare at your opponent while you fight him. the whole romanticism of "tracking" your opponent is naive at best: most weapons don't fire a continuous stream of bullets or projectiles, nor are the ones that do necessarily accurate past the first shot. as long as you know where your opponent is, you can minimize the effects of interpolation wrt splash damage by looking in a seemingly passive (or, if your opponent overly predicts you as a passive player, a hyper-aggressive) direction & committing to running towards it, turning & shooting only when you know your opponent believes you're doing something different from what you're intending. as such, it's very important to constantly practice predicting your opponent given a limited set of visual information. an exercise i regularly do is to plant my crosshair in one position (either on the map or constantly relative to my opponent) & attempt to make my opponent go where i want.
taking this a step further to a possibly unpopular opinion, i believe most higher level players in any game don't actually physically "track" their opponents regardless of what they articulate. as long as your modeling strategy is accurate, the closeness of your crosshair placement directly correlates with the precision of the resultant predictions. it's simply not physically possible to truly track your opponent in the long-term; physical tracking is essentially equivalent to tunnel-visioning, and you need to do it as absolutely minimally as possible.
a lot of this may become more intuitive when you optimize your physical setup to reduce aberrations and discomforts in edge-case arm/wrist positions. monitor refresh rate & mouse/keyboard actuation force aside, this requires a serious look at your posture & your setup's ergonomics. determine how much of your mousepad you actually use, and then further determine if those bounds are caused by physical/mechanical problems or from habit. determine if expanding your usable space would allow you to hit wider, previously uncomfortable shots. in total, make these analyses from your opponent's perspective: determine possible physical positions that you could take (wrt mouse placement and in-game camera angle) that would most likely be extremely uncomfortable for your opponent, and then make said positions as comfortable as possible for you.
more advice than that would honestly require me to watch you fight, but i think as long as you shift away from pattern & rule-based thought processes into a probabilistic mindset, you'll eventually consistently outplay your opponents. don't fall into intrusive thought feedback loops about "thinking too much" or "overthinking the situation": try to explicitly articulate what you believe your opponent is intending on doing wrt the type of fight & your relative spawn position, and make clear statements about what you're going to do when fighting your opponent. always approach your 1v1's with self-awareness. with enough cognitive practice, you'll be able to increase your mental & physical stamina. it helps to approach MGE with the end-goal of lessening your physical burden in more extreme applications (e.g. handing multiple opponents at once in 6's).
the best class-nonspecific ammomod-specific advice i can recommend is to play very aggressively since keeping momentum is much easier than acquiring it. nosplash is also a great precursor map to ammomod (although in ammomod it can be optimal to not direct your opponent's feet since splashing down at the ground is easier than directing your opponent in the air). if you're a soldier, swapping between your rocket & shotgun can stifle your opponent greatly (although i don't think it's necessarily good practice unless you have no confidence in your hitscan). you should also practice juggling your opponent with singular rockets: knock them up in the air, predict where they're going to land, shoot once they touch the ground, rinse & repeat.