The show itself used quite a few very interesting methods to do it. Basically, L played a lot of hunches and won big several times.
The part about the time of day was found out long after L had narrowed things down to a small region of Japan by provoking Light into killing someone who appeared on a "worldwide" broadcast that was actually only broadcast in Light's prefecture. The time of day part was actually used to hypothesize that Light was a student, whereupon the pattern changed to show people killed every hour of the day. And L saw through that by assuming (correctly) that Light had access to police data. It seemed like he was always watching Light's reactions to his moves, rather than the moves themselves.
Probably one of the most clever traps of all was after they met in person, when L was able to trap Light by getting evidence that Light knew something he should have no way of knowing at all by means of false evidence. He played it off as Light being too dumb to figure out the riddle, but the only reason he couldn't solve it was because he thought the answer was impossible (and he shouldn't have known that).
One problem with the article I realised earlier was that it described the broadcast to Kanto as a gamble because it wasn't broadcast anywhere else, which is wrong. It was broadcast in each region one after another to find out which region it was in. It wasn't a gamble at all, it was a very clever way of finding out where Kira was watching from.
It might be possible for him to hear about the broadcast by other means had he not been in the first region where it was broadcast.
But it never really turned out to matter, as you say. L was able to notice that weird case where the evil guy who had taken school children hostage died of a mysteriously timed heart attack and piece a lot of things together.
Actually, though, that broadcast was probably one of the most important puzzle pieces. He was able to prove that Light could kill remotely with nothing but a face & name, having cut a special deal with a criminal and kept the guy under special observation the whole time. Light was very careless there.
It would be extremely hard (probably impossible) to hide the fact that you need a criminals name and face to kill them. At most he could've gained a bit of time by being more careful, and at that point he didn't believe the death note would work anyway.
Maybe if you assume that psychic killings are possible from the outset. While people might be able to figure out that something is going on, proving that someone is doing the killings remotely via a notebook is quite a leap and only the crazy arrangement L tried made proving that possible.
The part about the time of day was found out long after L had narrowed things down to a small region of Japan by provoking Light into killing someone who appeared on a "worldwide" broadcast that was actually only broadcast in Light's prefecture. The time of day part was actually used to hypothesize that Light was a student, whereupon the pattern changed to show people killed every hour of the day. And L saw through that by assuming (correctly) that Light had access to police data. It seemed like he was always watching Light's reactions to his moves, rather than the moves themselves.
Probably one of the most clever traps of all was after they met in person, when L was able to trap Light by getting evidence that Light knew something he should have no way of knowing at all by means of false evidence. He played it off as Light being too dumb to figure out the riddle, but the only reason he couldn't solve it was because he thought the answer was impossible (and he shouldn't have known that).