On page 1037 of the Cambridge Grammar:
In [2iii] and [2iv] above is shown a gap "in object position".
In fact, this is where all the grammars that I know of would put the gap. If the gap corresponds to an object of a verb -- as here -- or of a preposition, all the grammars that I know of put it after the verb or the preposition.
But I wonder why it has to be.
If you look at [2ii], which is used instead of the gap in [2iii] or [2iv], and that which is also acting as an object there. But it isn't placed after gave me but is placed at the start of the relative clause.
Since the gap you can't see anyway, I wonder why the gap cannot be placed right before my, as follows:
I accepted the advice [that ____ my neighbour gave me].
I accepted the advice [____ my neighbour gave me].
This way, I think the structure of the relative clause might be more coherently explained and understood.
Also, does anyone know of a grammar that places the gap like this?