SS-picture, SP- is
SS- He, SP- been
SS- lights, SP- went
SS- bookcases, SP- were
The simple predicate is the subject of the sentence, or the person or thing that is performing the action of the sentence.
The simple predicate is the action being performed by the subject, usually just a verb.
Make sure to note what action is actually happening in the sentence.
For example, "The picture I want to buy is here."
The sentence is about the picture, not you wanting to buy it.
This means the simple subject is "picture," and the simple predicate is the verb that the subject does, so the predicate is "is."
It is easier to imagine the sentence without the "I want to buy," so it just reads, "The picture is here."