I'll try to explain. "протянул руку вдоль взгляда" - it can have some sence, but sounds very wierd. "he reached out along (his?) gaze"? I'd never say that. "в направлении взгляда" sounds more like it.
Now the word "забранного" is a mess in itself. It obviously derives from "забрать" - "to take something away", but itbis actuallybused onlybin one context "забранный решёткой" - "covered by a grating". it can be said about a tunnel, orca hole or somesuch. Now if we want to talk about something that has been taken away, we would say "который забрали", not "забранный". and when youvtry to apply any of these meanings tovthe word "взгляд" it just doesent fitveither way.