Tips:
Press Shift to use stamina. As engineer this let's you run fast. As a general rule of thumb use stamina to run to broken components, guns, or to save a critical component from being destroyed. Stamina refills over time and there is bonus refill when your ship gets a kill, or as engineer when you rebuild a component.
Spanner repairs one bar of health (20 HP) and mallet repairs 5 bars (250 HP). If it's only slightly damaged use the spanner to repair. After you use the mallet move to another component because mallet has a nine second cooldown. Unless you are tanking a critical component, constantly move around after you mallet.
In the bottom right on the left side of the hull indicator you can see the current pilot tool being used.
Goldfish:
As engineer on goldfish (not the most exciting job) you will be constantly moving around and repairing. A good goldfish pilot will burn their engines the most of the match so there isn't any free time.
Rebuilding the side guns is the last priority. If there are multiple broken components don't worry about side guns because all other components are more critical. The right side gun is generally more important because it's closer to the hull. The idea is to shoot the front hwatcha then spin to a side gun while the hwatcha reloads.
You can jump from the balloon to the bottom turning engines. You did this on the left side, but it's much faster and easier to do it on the right side next to the balloon. If the other engineer is already repairing a component, don't follow them. You may help rebuild but you shouldn't help repair.
Your pilot is an experienced goldfish pilot and did good besides not burning enough engines, probably because he was worried about repairs. Hopefully you'll find a good captain who uses a mic, and fly on something more interesting than a goldfish.
Find a captain with a mic who gives you a recommended loadout and assigns you a position.