Forewarning: this is pretty much directly aimed at my players from last night and last campaign. Time to lay down the law (and for mercenaries my world over to grow a pair and refuse to be treated as expendable).
I think the critical passage from the rules, with regards to the treatment of mercenaries is this:
Mercenaries are generally hired to garrison a stronghold or wage war in military campaigns. Mercenaries will not accompany their employers on highly dangerous adventures such as dungeon exploration unless they become henchmen. The Judge should determine what constitutes a military campaign and what constitutes an adventure depending on the overall circumstances.... Mercenaries in garrison need only be paid their wages, but mercenaries on campaign will expect a share of military plunder in addition to wages.
ACKS Core, page 51.
Thus we've established that mercenaries may "generally" be employed in two situations - defense of a garrison, or "on campaign". Campaign is something of a nebulous term, but it seems we can set up a dichotomy with the DaW:Campaigns rules (which seems a definitive source, by its naming):
Each participant [in a battle] (whether a commander, a hero, or a creature in a unit) earns 1 XP for each gold piece he collects from the spoils of war. Troops will expect that at least 50% of any spoils captured will be shared on a pro rata basis in relation to their wages. If this does not occur, the Judge should make a morale roll for any unpaid troops [note that a Fanatical Loyalty result from a morale roll due to lack of pay is instead reduced to Loyalty; mercenaries may never gain morale by lack of pay].
For ease of play, troops’ XP can be tracked on a unit-by-unit basis. 0th level characters can be advanced to 1st level as per the rules in ACKS under 0th Level Characters and Experience from Adventuring (q.v.). In general, it requires 100XP for a 0th level character to become a 1st level fighter.
So: if your mercenaries are not in garrison, they must be on campaign. If they are on campaign, they will demand significant spoils and earn XP accordingly. There Ain't No Such Thing As A Free Force Multiplier. If it seems ridiculous for your number of mercenaries to be demanding a collective 50% of treasure earned, then you don't have enough mercenaries for it to be a campaign, and you are on an adventure instead, in which case they're not coming with you. Note also that untimely termination of mercenaries in order to avoid paying them (or comparably "letting die", by putting them in positions so risky that neither PCs nor henchmen will willingly join them) is liable to generate some discontent, betrayal, or general bad karma. Don't be the blue guy, and recall the fate of a previous Scarth.
With that out of the way, what are some reasonable rules of thumb for adventure vs military campaign (besides number of mercenaries)? From an examination of actions in which mercenaries have been involved in my games, it seems to me primarily to be about the structure of the opposition. You say military campaign, I hear "massed enemy troops", which usually implies humanoid foes. Bombarding an orcish encampment is a military operation, as is storming a weaselman village or beseiging a troglodyte lair. These are foes that a normal man might fight and hope to best in single combat! And foes against which conventional military training, doctrine, and formations are effective. While they may have the occasional witch-doctor or warbeast, those are adventurer problems, and mercenaries met with such a foe are liable to run (ex: in DaW, units of troops coming under the effects of enemy magic must immediately make shock rolls. That's the degree of tolerance Joe NPC Fighting Man has for fantasy). The proper application of mercenaries is to problems where an individual enemy is not much of a threat to the PCs, but the sheer number of enemies is too great for them to deal with individually.
A dragon hunt, however, is (very clearly) not a conventional military campaign. You cannot hope to hunt a dragon with a phalanx of pikemen. You cannot lay siege to a dragon's lair, for when night falls, it will break out (or perhaps just eat your sentries). Any individual mercenary against a dragon will be lucky to strike a single blow before being vaporized. This situation is very much counter to a mercenary's priorities, namely "stay alive, get paid, keep staying alive to spend the pay" (as we saw with our >50% mercenary casualties... and you didn't even bother to check 'em for mortal wounds / attempt first aid. See, that's the sort of thing that spoils employee relations).
No, if you want to bring mercenaries on your dragon-hunts (or wyvern-hunts, or catoblepas-hunts, or most-any-beast-scarier-than-an-ogre-and-even-that's-pushing-it-hunts) in future, you will need to hench them, per the standard henchman hiring process (though refuse and slander is more likely "refuse and leave service", and circumstantial modifiers for level of risk and prior treatment of both mercs and henchmen may apply). Further, as a clarification, henchmen of henchmen shall receive one-sixth of a share of GP, but only a quarter of a share of XP (it has been observed that if provided a half share of XP, they will catch up with their employers in a way that first-tier henchmen do not; thus this internal inconsistency is avoided). Likewise sub-sub-henchmen receive one sixth of a share of GP, but only an eighth of a share of XP, and so forth down the chain. Be aware that while hench-chains permit you many more hirelings, if one of your direct henchmen leaves your service, his henchmen will as well.