If it doesn't have intelligence, then you always have to push it with handle animal to do a trick (which needs a check).
Animal companions get bonus tricks though, so that is one way to get them to 'learn' tricks. Also, you can put their ability score increase into INT, which would give 3 more tricks.
But past that, there isn't anything that immediately comes to mind that helps in thsi endeavor. It is just the price of having the mindless trait.
Not quite Lemeres. Mite's have a special ability.
Vermin Empathy (Ex)
This ability functions as a druid's wild empathy, save that a mite can only use this ability on vermin. A mite gains a +4 racial bonus on this check. Vermin are normally mindless, but this empathic communication imparts on them a modicum of implanted intelligence, allowing mites to train Medium vermin and use them as mounts. Vermin empathy treats swarms as if they were one creature possessing a single mind—a mite can thus use this ability to influence and direct the actions of swarms with relative ease.
Now the weird part is that don't have any innate ability to get animal companions, and without a statement about what to treat their int as they don't actually have a number of tricks they can learn.
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Lemeres: for animal companions: Mindless quality from ultimate magic: : Vermin companions have no Intelligence score and possess the mindless trait. In spite of this, vermin companions may learn one trick, plus additional bonus tricks as noted on Table: Animal Companion Base Statistics. If a vermin animal companion gains an ability score increase (at 4 Hit Dice, 8 Hit Dice, and so on), the druid can apply this increase to the companion's Intelligence, changing it from — to 1, at which point the companion loses the mindless quality and is able to know up to 3 tricks per point of Intelligence, plus the additional bonus tricks, as per Handle Animal. Vermin companions have no skill points or feats as long as they have the mindless quality.
Here's how I've always worked it: Vermin Empathy is like Wild Empathy. That ability allows druids to "push" an animal as a Move action. I then give mounted mites ranged weapons they don't need to use a Move action for, and then justify them pushing the vermin every round to commit the creature to its trick.
Alternately you can use a little fuzzy logic on the mites' Vermin Empathy ability itself. "...allowing mites to train Medium vermin and use them as mounts" from Claxon's quote above. This suggests the creatures are trained to bear a rider.
Under Animal Handling there's a 3 trick suite under the general purpose: Riding. The animal so trained learns Come, Heel and Stay. These 2 pieces taken together suggest that, when Vermin Empathy is used it imparts roughly 1 Int for the purposes of the training.
If instead you want to say that the mites train their vermin with 3 other tricks, say Aid, Attack and Guard, that would be a nice little bevvy of useful abilities to call out as a Move or Free action depending the action you rule they have to use for Vermin Empathy plus Handle Animal.
Personally I look at it like this: I've NEVER gotten all nit-picky over the dude that runs a Hunter in my homebrew game. As such I don't brook any rules-lawyer player getting on my case b/c "Vermin don't HAVE Int so how is the mite making him do all this cool stuff like Charge, then Withdraw, then outright fleeing and hiding, followed by another ambush one room later huh?"
That's usually when I add a pit trap right under that guy's PC...