I've been messing around with a theory I've had for a while and I think I'm confident enough in it being true to make a big infopost about it. Let's talk mounting mechanics.
I'm sure most folks have noticed how mounting seems weird and inconsistent. Getting the mount is no problem, those mechanics are well known and work consistently. The trouble arises once you're rodeoing that sumbitch. Sometimes you'll get a finisher right away, sometimes it'll take forever and finally you'll get one, sometimes you won't get one at all and the monster will just fall over, seemingly of its own accord. Well, I have an explanation, which is born out by all the testing I've done so far. From what I can tell, there are two things going on when you mount the monster: Part threshold and Monster threshold (names are just bullshit I made up). Part threshold builds via attacks to whichever part of the monster you are riding/hitting at that time, whereas monster threshold just builds via any damage the monster takes while mounted. If you max out the part threshold, you get a finisher. If you max out the monster threshold, the monster just falls over. From what I can tell, the white circle around your map tracks the monster threshold.
So what does that all mean, in practice? Well basically, in order to get a finisher as fast as possible, you want to maximize the mount damage to a single part of the monster. If you hop around all willy-nilly, you aren't going to be maxing out any particular part threshold and have a good chance of just knocking the monster over before you can get a finisher. This is relevant because a trick I'm sure most people picked up pretty quickly is hopping to another part of the monster when it tries to shake you off and continuing to attack. However, it turns out this is actually counterproductive because all you are doing is starting over on a new part threshold, while the monster threshold is still building. What you should do instead is go back to bracing when it's simply a shake and only moving when the monster is ramming terrain (which will automatically knock you off). In the latter case, you also want to jump back to where you were before after the monster does its move. Once I started bracing again, I got finishers a LOT more consistently.
There are some other factors at work however. Firstly, it seems like any damage the monster takes (from allies, palicoes, or even other monsters) while you are mounted contributes to the monster threshold. This is pretty noticeable in good 4-man groups where everyone keeps attacking after a mount. Usually the monster will just fall over all by itself in pretty short order, way before you could get a finisher normally. What is a lot harder to tell is if damage to specific parts from other sources (like allies etc) contributes to part threshold. That I haven't been able to prove one way or another, you'd probably need to get some buddies in with bowguns or something and test it specifically. It also seems like the thresholds are increased for multiplayer hunts, which would be logical. Another issue is that the monster is still susceptible to CC effects, flinches, and staggers, most of which will interrupt the mount (the exceptions that I've noticed being shock traps, the vine traps from fallen trees, and I think paralyze effects). Since palicoes do a surprising amount of damage (not to mention a lot of their gadgets causing flinches), it's very possible for them to interrupt mounts all by themselves.
One final thing. I would often see the prompts to pick up slinger ammo while mounted and so in the course of all this I decided to do some testing. It turns out that most slinger ammo does a BOATLOAD of mounting damage when you are rodeoing a monster. Since you can shoot your slinger while mounted and it shoots it directly into whatever part you are on, it turns out that the stronger slinger ammo is AMAZING at getting you mount finishers quickly. In particular, Scatternuts and Crystalburst will both stagger the monster and build a LOT of threshold, so much so that in solo hunts just one shot will often instantly get you a finisher. This is obviously super useful since it takes getting a mount from a DPS loss when solo to a huge gain, since you cut your riding time down by like 75% or more. The ammo to keep an eye out for is the aforementioned Scatternuts and Crystalburst as well as the monster-dropped Bomb Pods, Thorn Pods, and to a lesser extent, Pierce Pods. These all seem to do huge amounts of threshold damage and also will all stagger the monster, interrupting whatever it is doing (such as trying to knock you off). They make mounting WAY faster and more reliable. The other ammos don't seem to have nearly as much of an effect, they still do damage to the thresholds but I don't feel like they're noticeably faster than simply knifing away and they don't give you the useful stagger/flinch.
Putting it all together, what I've been doing is grabbing some Scatternuts or Crystalburst immediately upon starting a quest (as long as it's relatively convenient to do so). Then when I get the mount, I'll jump to the head and instantly shoot the monster in the face with my slinger. Generally that gets me the finisher then and there and I can proceed with the hunt, very occasionally (only happened twice in over two dozen hunts) it'll take two shots on that first mount. Later, if I happen to get a second mount, I'll either use the rest of my ammo, or some Bomb Pods or Thorn Pods that I've picked up. Thorn Pods are particularly cool because you can shoot both of them into the head and then you'll blow them up with your finisher immediately after, doing a grip of damage and KO.
TLDR: Focus your attacks on one part when mounted to get a finisher faster. Use slinger ammo that causes a flinch (Scatternuts, Crystalburst, Bomb Pods, Thorn Pods) to stagger the monster and get a finisher really fast.