Glad you like the site!
It really depends, they (NAPPI) have taken great strides in revamping the flight school training process. They basically worked backwards, from the Fleet backwards to API. (This is all coming from a brief we got the opportunity to sit through back in Primary from the consultants the Navy was hiring, NAPPI, to streamline everything). I was very fortunate, and throughout all my training to date, I have not waited more than a month between training.
But to answer your question (and contrary to what Dave says, I still have a lot to learn! ), stash jobs are usually handed out during the pool waits, if they tend to get lengthy, there are a bunch of people milling around in the pool, or they need a warm body to fill a job.
Stash jobs can range from working at the Naval Aviation Museum in Pensacola, to helping out in Student Control, or getting farmed out to one of the VT Squadrons as manpower, usually you end up helping the PAO and admin in those situations.
In addition to stash jobs, there are other one time event jobs that come up, and during pool waits you get hit up for, these can range from pubs duty (updating pubs, oh joy), helping out at a sporting event (handing out water at a run, etc...), guide visitors around or be availble to visitors at a static display of the T44/T34, and the list goes on.... If the powers that be notice that there is an inordinate build up of manpower sitting out at the pool each muster day, that means they will usually find something for you to do! Sh!t generally rolls down hill also, they will usually take "volunteers" in the following order: Pre API studs, Post API studs, Primary studs, Advanced studs, then finally the Winged studs. So in effect you usually pay your dues early on.
On occasion I have heard of some guys requesting TAD orders to a specific unit, but that really depends on the length of the wait between training, and if the training command is willing to release you.
Hope that helps!