Custom Camera for Spaceship?

Currently, I am at loss on how I can make a custom camera work for an object in-game apart from the player. I am attempting to create a dynamic camera that uses how the camera works for a third-person player in-game for just one object (similiar to spectating another player), albeit it seems that it will require an immense amount of programming. Even though I am a programmer myself, I don’t know the correct approach to this situation.

I want this camera movement:

To be implemented for this spaceship:

I’ve looked for something remotely similar to this issue across plaforms such as the DevForum itself, YouTube or other forum websites. There is probably something covering this already, although I looked everywhere I could have possibly found something to no avail.