Quod cum...fecisset,

In LLPSI Cap XXXVII Orberg Scripsit:

Aeneas autem per tenebras errans coniugem suam quaerebat; quin etiam clamare ausus est maestusque ‘Creusam’ iterum iterumque vocavit. Quod cum diu nequiquam fecisset, imago atque umbra ipsius Creusae viro stupenti apparet et his dictis eum consolatur: “Quid iuvat me lugere, o dulcis coniunx?”

What’s the meaning of ‘Quod’? Does the sentence mean: ‘Which when after a long time trying in vain.’ ? Is ‘Quod’ a neuter pronoun referring to the ‘thing’ he’s trying to accomplish - i.e. find his wife..?

Yes, it’s the neuter pronoun, “which thing”.
Ut dicis, pronomen neutrum.

Gratias tibi ago Adriane.