Relative clause (reference of "which")

Question

They've asked him to mend the fuse, which he won't even try.

From The Cambridge Grammar of the English Language, which deems it as ungrammatical, without further explanation. I think that "which" could refer to "to mend the fuse": which he won't even try = he won't even try to mend the fuse.

Do I get it wrong？Could you please tell me how to revise the sentence?

Context (summarized from the book):

1. They’ve asked me to mend the fuse, but I can’t.
2. They’ve asked him to mend the fuse, but he won’t even try.

The relative counterpart for (1):

1a. They've asked me to mend the fuse, which I can't.

But there is no comparative counterpart for (2).

2a. *They’ve asked him to mend the fuse, which he won’t even try.

Answer 1

The meaning of the sentence is clear, and it might even be used in casual speech. I think the problem is that, strictly speaking, which appears to refer to the fuse rather than the action of mending it (he won't try the fuse). It would be more correct to say:

They've asked him to mend the fuse, which he won't even try to do.

Does this make sense in relation to what your grammar book is discussing?

Answer 2

"To mend the fuse" is an infinitive phrase acts as an adverb modifying the finite verb "asked". If this is followed by a relative clause, the relative clause can only modify the noun it follows i.e. the fuse. A relative clause cannot modify an adverb.