Your backup lights route thru the "neutral safety switch" NSS on most automatic transmissions. However, if you have a floor shifter, the NSS is there, at least in early cars. What year is your car?
Needs a better translation. Makes no sense to me.
Do you mean "relay"? Don't recall any in the backup light circuits.
Describe your car. Sounds like maybe a manual transmission. Is that the "box" you speak of?