The rules themselves, when comprehended as intended.
Cool. Just shoot me a link to the developer content stating this intent, and we're golden.
Straight after a (long) rest, you do nothing but stare at paint drying for 45 minutes. Is that 45 mins of rest 'short resting' or 'long resting'?
If by "straight after a (long) rest," you are meaning "after having rested for 8 hours", then the 45 minutes watching paint dry is part of - not after - the long rest in question. Because a long rest is at least 8 hours, not 8 hours exactly.
If it's 'long resting', 15 mins later (when it's been 1 hour since my last stressful activity) do I gain the benefits of a short rest? Of course!
There is nothing in the rules text which supports not having to choose which sort of rest you are taking, and thus nothing which supports being able to treat the 8 hours minimum that a long rest is made up of as being 8, or any other number of, "at least 1 hour" short rests.
'Resting' doesn't have a type (long or short) attached to it, because 'resting' is not an activity! 'Resting' is a lack of activity. 'Resting' is not 'doing something', it is not doing something.
The language and layout of the rules text is in direct opposition to your claim. You are using the standard definition of rest, but the game has made its own definition of rest, so the standard definition does not apply.
At the end of a short or long rest, you gain the benefits. But when is that, considering that the rests are 'at least' 1/8 hours?
The answer to "When is that?" is simple; When you do something besides continue to rest.
Imagine you are doing nothing strenuous for 16 hours. When do you get the benefits of a short rest? Long rest?
At the end of that period of time, just before you do something that doesn't count as resting, you get the benefit of whichever type of rest the player has chosen for it to be (though I can't say I can think of a reason why a player would do what is fully within their power and take a 16 hour short rest instead of a 16 hour long rest).
The way you see it, since the long rest is 16 hours here, then you don't get the benefits of that long rest until the end of the 16th hour. Why?
Because that's what the words in the rule book say.
Why don't you get the benefits after 8?
Because the rule book defines a long rest as "at least 8 hours", which is different than had it said "8 hours."
How does your body know not to give you the benefits after 8 hours?
There is no body in question. Characters are not real and do not have bodies. The rules of the game are not the physical laws of their world, they are only device by which us real folk can play a game, and need not be considered in any way other than that.
The way it works is this: one hour after your last stressful activity, you gain the benefits of a short rest. Why? Because you have fulfilled the short rest conditions as set out in the PHB.
Actually, the way it works seems more to be that the players declare their intention to rest, and the DM covers what happens - whether that is the passage of time in which rest is successfully accomplished, of the sort chosen and declared by the players, or events that interrupt or otherwise alter the outcome of the players' declaration.
There is no text in the book which suggests I am actually supposed to be watching the in-game clock to see how long it has been since the last activity not allowed during a rest, and handing out the benefits of a short rest at 1 hour or long rest at 8.
In fact, it is quite the contrary since a single spell cast 30 minutes into a short rest spoils the the rest entirely, but a single spell cast 30 minutes into a long rest doesn't interrupt the rest - clearly supporting the idea that one must choose the sort of rest they are having their character take at the moment they decide they are taking rest.
If you have fulfilled the conditions for a short or long rest, as set out in the PHB, there is no rules reason to deny those benefits as given by the 5E rules.
I haven't agree with that. I have agreed at what exactly it takes to have "fulfilled the conditions for a short or long rest, as set out in the PHB." Specifically that resting for another hour, or longer, after you've supposedly ended a long rest is not fulfilling the conditions of a short rest, but merely ending your long rest an hour later than you supposedly have.