I'm going to go full retard on this explanation.
Caffeine does take at least an hour to take effect, for some of us it will take closer to 3 hours from consumption to have an active effect and that gets worse as we get older. This can lead to dose stacking as people will consume a lot trying to wake up.
For most of us caffeine will have continued effects for 8 hours or more (fits with that half life). Some of us will be slow caffeine metabolizers and it will take 48 hours to clear our system, such people should just give it up. 1 in about 10,000 will by a hyper-metabolizer, these are the rare people that truly can drink it all day as they clear it in about 3 hours. Notice, most of us probably don't even know someone who fits into that category, even less likely that we are one.
Genetic testing can get to the short answer. If you have money, WildHealth provides some good services. For the rest of us, we can figure it out by experimenting.
Caffeine is subject to tachyphylaxis (fancy way of saying we get use to it after a while and the effect greatly diminishes), however the degradation in sleep quality is not one of the effects that diminishes. After 48 to 72 hours of caffeine deprivation tachyphylaxis will no longer be present. One way to finger out how you metabolize caffeine is to strictly avoid it for 3 days, then consume a decent bit, then see how long it takes for the effects to wear off.