What's the "appropriate" amount of time? Is there one?
The thing is, this is a country kid in the middle of nowhere. I've never lived that way, but I can imagine it's very different than if a 4 year old went missing in a country town, suburb or busy city.
In his situation, there's likely no thought of him being snatched, readily getting into a car with someone, wandering into another property, walking to the shops, following a lost dog etc like city people might immediately think. I'm sure your mind doesn't immediately go to dark places in this situation. You'd automatically assume he was hiding or had wandered off, nothing nefarious. MOO though.
Now we don't know how many people or adults were at the property when he went missing. Maybe it was just Grandma, maybe many. Either way, I'm sure they all started searching the standard places. Those places could be many just within the area around, and within, the home. Aerial shots show lots of structures and photos show bits and pieces around the yard and immediate surroundings. You'd probably start with a quick search, calling his name. Then when he wasn't found , you may check the same places but more thoroughly. You may even do it a third time, or have someone else search this same places really thoroughly, searching in every possible book and cranny that he might possibly in.
Then you need to search wider, maybe looking into water holes, under bushes etc. All this takes time, especially if Grandma was alone.
I don't think we can judge what we'd do in a similar situation, especially without experience having lived remotely. I think it's a whole different ball game to a child missing in an area that is built up and has a huge amount of foot traffic, not to mention vehicle traffic.
