Gat
Try to make all the shots hit armor by avoiding shooting near components. Against a pyra this means aiming at the lower section. There are situations to aim for components, but if you're trying to kill then avoid hitting anything except armor. Reload as soon as you break armor. Most ships will rebuild their armor by the time you reload and it's a waste to shoot gat at broken hull. By reloading and holding fire you maximize DPS to armor
Mortar
You should often shoot before their armor breaks. Against low-armor high-hull ships like goldfish, spire, and squid you should prefire early to break armor faster and maximize hull damage (they rebuild quickly). Against squid you can start shooting when the gat starts. Another tactic is to count the number of mortars you need to kill and save that many for the armor break. Default mortar deals 126 dmg so against a pyra you can immediately shoot 7 and keep 5 in reserve for armor break. Each mortar does 27 armor dmg, so 7 shots will break 29% of a pyra's armor.
If the gat won't break armor on the current clip, shoot the mortar until gat reloads, and then reload. If armor doesn't break, reload as soon as the gat reloads because mortar has a one second longer reload (6 seconds). If the gat is nearing the end of the clip, shoot until gat reloads (unless armor breaks). If armor breaks and is rebuilt before finishing the mortar clip, reload if you don't have enough shots to kill or if it'll be 5+ seconds until the next armor break. In most cases you can hold fire instead of reloading if you have half a clip and expect a quick next break.