Confusion on use of だった with sentence that uses nominalized verb


I'm reading a book and have come across this sentence

> アニーが指さしているのは、一本のなわばしごだった。

I know this sentence translates to something like

> Annie was pointing to a long rope ladder.

But what I truly don't understand is what does the だった at the end modify? Is
it modifying アニーが指さしている (Annie pointing) like I believe?

Or is it really modifying 一本のなわばしご (rope ladder)? And the translated sentence
is more like

> Annie pointed to what was a long rope ladder




This is a rather simple example of [a cleft
sentence](https://japanese.stackexchange.com/a/19208/5010).

> アニーは一本のなわばしごを指さしていた。  
>  Annie was pointing to a long rope ladder.
>
> アニーが指さしているのは、一本のなわばしごだった。  
>  It was a long rope ladder that Annie was pointing to.

Grammatically speaking, だった is modifying nothing.

Note: This `の`/`it` is referring to a tangible object, so in this case, it is
possible to translate the sentence using the simple grammar of relative
clause: "The thing (=の) Annie was pointing to was a long rope ladder." But
cleft sentence is a grammaticalized concept that has a wider range of usages.




This is a rather simple example of [a cleft
sentence](https://japanese.stackexchange.com/a/19208/5010).

> アニーは一本のなわばしごを指さしていた。  
>  Annie was pointing to a long rope ladder.
>
> アニーが指さしているのは、一本のなわばしごだった。  
>  It was a long rope ladder that Annie was pointing to.

Grammatically speaking, だった is modifying nothing.

Note: This `の`/`it` is referring to a tangible object, so in this case, it is
possible to translate the sentence using the simple grammar of relative
clause: "The thing (=の) Annie was pointing to was a long rope ladder." But
cleft sentence is a grammaticalized concept that has a wider range of usages.

