Just how long do you think there should be between initiations in game time? Weeks? Months? The only thing I could find in the books is a comment saying it could takes months for a some people to figure out a point of magic theory. Does this mean months is normal?

I want more then a comment saying as fast as they can pay for it.

This isn't going to be that help full but, I'd say it should be when they have taken a step forward in knowledge. Hard to ref i know but it suits my game. I generally encourage some increase of related stuff(magic, the skills, relavent attributes) between initiation, to represent the character using their new insights.

From a fluff point of view I think years should pass between initiations.
Of course, this is impractical for the actual game.

But IMHO initiation, especially the first time, is a world-shaking event for a magician.
I guess a majority of magic users never initiates because they lack knowledge or courage or both.

A rather extreme, but fitting IMHO, example of a high-rank initiate is the racoon shaman "Bandit" who appears in several SR novels - he is almost completely detached from real life, follows the way of his totem without compromise and has severe problems interacting with mundane people.
IMHO a magician gets more and more excentric and somewhat autistic the more he initiates - his life revolves solely around his magic, anything else is of secondary concern.

Why wouldn't a Mage initiate as often as they can? Most mages spend most of their effort (karma) learning as much as they can about the Art. Many are driven to go as far and as fast as they can to become better at Magic, and as soon as they learn that initiation will improve their abilities, they will likely be focused on it.

It was my understanding that magic groups only meet every so often. I would say you could only initiate as often as your group meets. Other than that, it is whatever fits your character and style of play. I would encourage the player to develope other magical abilities between initiation, but I don't think I would be quick to inject houserules by putting limits on it. It is probably like most things in life, if you put in the extra effort, you'll advance at a quicker rate than the norm. I was also under the impression that only about 50% of magicians initiate, but that's just how I always viewed it.

Magical groups might not initiate as quickly since to do it as a group, it helps that everyone is 'ready' to progress onward. (which becomes increasingly easier with a 40% discount if you throw in an ordeal every time). However, a solo Awakened might initiate pretty fast if, as mentioned earlier, they put all things secondary.

mechanics wise, I would see intense study and effort being cash spent on rare tomes or magical boosters (which emulates cash for Karma). I could see a twistd path alternative to that being the theft of power from Foci and similar magical items (though I would think that would have a nasty drawback to it, like a permanent link from you to the owner of the foci you sapped.)

Also, there are two paths of magical dedication: Path for Power, and Path for Knowledge. Power is focusing almost solely on initiation and your magic attribute. If you're not spending on things like spells or skills or otherwise, it makes sense you'll find someone a bit more advanced in those if they shirk everything else. Knowledge would include spells, foci, training other Awakened (if you're the teacher sort), formula designing to make a better version of a spell, etc.

Finally, the last reason you might not see a lot of initiation at first is that the Awakened world aren't all at 4+ Magic. A lot are low level folks with 1's, 2's, or maybe a 3. They're not going to initiate as often, because if they want a bit more bang for their buck, boosting their magic attribute is a better deal at the time. Then they have to make a living, pay rent, etc...

I guess if you're a fanatic of learning or a Shadowrunner that does a lot of karma-building stuff, you're one of the exceptional few that hits the lime light.