mens cogitet eius id ipsum

Lucretius, Book 4, Lines 779-780

Lucretius is explaining his theory on how visual images are produced, how people have visual images in dreams, and even at will. He say there is much to be cleared up about this.

Quaeretur in primis quare, quod cuique libido,
venerit, extemplo mens cogitet eius id ipsum.

It will be asked in the first place why, when a fancy comes to it
immediately the mind thinks the thing itself, of itself (the mind).

What I can’t parse is “eius id ipsum”. My guesses follow.

id: “the thing”, the antecedent is what is fancied
ipsum: intensive complement of “id”
eius: genitive, singular, complement of “mens”

Forsit (verbatim) hoc:

It will first be asked why, as often as the desire for whatever thing comes, the mind would immediately picture that very one of it = precisely the very thing

Thank you adrianus.