Open conditionals are used when the speaker thinks it possible that the "if" clause is true. You might use a past conditional when giving an instruction.
(teacher) Yesterday I gave everyone a book to read. If you started reading your book yesterday, please finish reading it now. If you didn't start reading your book, I want you to do a maths problem.
Or simple conditionals like
If you started reading your book yesterday, you know that the main character is called Paul.
Compare that to the "second conditional":
If you started reading your book right now, you would find out that the main character is called Paul.
Which presents an unreal situation (you didn't start reading) but is speaking about a non-past time.
The "first, second, third" pattern of conditionals is a simplification, to help learners understand that past tense in conditional expressions doesn't always refer to past time. But not every conditional expression fits this pattern.
Your example is, perhaps, not very common. But it is correct. It would be better to use a present perfect, as there is a strong connection to the present state:
I've you've started reading a book, you ought to read it to the end.
I've also put a modal in the advice, for extra clarity.