That's always confused me- why does extinguishing start a cooldown where you can't repair? I can understand a cooldown where you can't extinguish again, but extinguishers initiating a repair cooldown is unduly frustrating in cases of new/bad engineers, AI engis DOOMING US ALL, and lag (occasionally I'll hit a part to repair it, then immediately after spray it with an extinguisher. For whatever reason, the repair may not register, but the extinguisher does, meaning I'm probably dead).
It just doesn't make sense that I can repair then extinguish, but not extinguish then repair. It actually seems more intuitive to extinguish then repair since the part will be at full health afterwards (doing it the other way around means the fire will probably damage it a little, so it'll be less than full health afterwards). You could argue that it's something you should know if you're any good, but nowhere does it tell you that or explain why it's even a thing. You have to discover it for yourself or wait for someone to eventually tell you why you're terribad.