Hello, Sharon! As I see it, the sentence says: The water tank (the reservoir for water in some equipment) started falling back and was reinstalled (reattached to the frame of the equipment) very precisely (with the skill of a plastic surgeon). Hope, it will help you.

Sharon, What word do you think is the subject of the sentence? Why do you doubt yourself? You can use the process of elimination and some logic. We know the subject comes before the verb The sagging back half of the water tank 'of the water tank' is a prepoditional phrase The sagging back half 'The' is an article sagging back half 'Sagging' is gerund Back half Back is adjective describing Half