(1) ALWAYS click on the next "target" as soon as our friend calls out "Ha!" after he has picked something up! That way he never wastes any time standing! Even when our hero is walking up the stairs to the house, you already click on the first destination!
(2) You can enter a room as soon as the neighbour is about to leave (one or two steps to the door he's taking)... Try to get a feeling when it's safe to come in, sometimes they're literally in the same room while operating the doors. Make it a tight squeeze, you need the time!!
(3) Waking up pets (at least the parrot) can be a tactical move to gain time: The neighbour will interrupt his routine to look after the beast and that can give you valuable seconds... Just remember to click your destination again after our friend has been shocked by the animal and has stopped walking! In fact, you can keep on clicking while he's freaking out-- that way you make sure he doesn't lose time!