I haven't finished my home work yet but I have reviewed accounts of 12 battles between 1775 and 1863, ranging from skirmishes to major battles. Nothing in the process has shaken my basic understanding of how things worked, the basis behind my rules, but I have answered the first question to my satisfaction. I have not answered the second question completely, the absence of examples not being sufficient proof that something didn't happen.
The first question was to do about how retreats come about and the answer seems to be a resounding "yes" to all of the listed possibilities. In short, sometimes when a serious attack is made, one side is defeated, the ranks are broken, discipline lost and the men run away.
On other occasions, one has what might be termed a "drawn" melee where one side has had the worse, suffered heavy casualties and/or had portions of the attack break and run. In these cases, local commanders may give an order to retreat in good order to save the remaining troops.
In fairly rare cases, the drawn melee may be evenly balanced and prolonged and an orderly retreat is ordered by the over all commander.
Assuming the player is over all commander, the first 2 are beyond his control and should be handled by the combat resolution mechanisms whether or not this includes a morale test, possibly for the commander rather than his men. It could be seen as a question of how badly the melee has been lost at an intermediate level. The 3rd is definitely a player decision. If the player is representing the free will and capabilities of more than 1 level of command, then a good case can be made to have the combat mechanism handle the fate of sub-units and leave the rest in the players hands.
Having written of my underlying assumptions or understanding about horse and musket warfare, this may be as good a place as any to set out the relevant parts.
1. There is a difference between artillery and skirmish fire and an attack. The only cases where even the worst troops are broken by such fire are rare enough that they can be treated as special events and shouldn't be incorporated as a possibility in normal rules. I speak here of troops breaking as opposed to a command decision to retreat the unit to a safer place. Note that if attempting to limit the player to 1 POV then, a mechanism for that decision to be taken out of his hands could be appropriate, a reaction test if you will for that specific circumstance. The resolve of troops can be however be weakened by such fire by more than the loss of numbers.
2. Exchanges of long range fire between formed troops other than as an early stage of an attack are rare enough that I still don't have a good feel for the issues but I suspect that this falls under the same rules as for artillery and skirmisher fire.
3. When an attack is launched, one side or other is sometimes broken or destroyed almost at once. In other cases a prolonged fight is required before either one side breaks or is ordered to retreat. A pursuit is likely to convert a retreat to a rout. By attack I am lumping together effective range musket fire as well as "charges". Even in the American Civil War with both sides armed with rifles, this decisive combat seems to happen at fairly close range, say within 100 yds and rarely last more than 20-30 minutes, say 1 or 2 turns. Within this process, there are clearly examples of the sorts of behaviour described by many traditional morale tests, troops firing early or unleashing a volley and running, atackers halting short or falling back slightly and then being rallied and led forward again. If looking at the over all attack though, these are all subsumed in the final result.
4, When a higher level formation launches an attack, the fortune of component units may vary but the generally either the whole fails or succeeds. It may be that when the first sub-unit on one side breaks, the surrounding units either panic or are forced to conform as a matter of self defense, regardless of orders.
5. If a unit is broken in combat, it is generally finished for the day even if part of it rallies. If a unit retreats without being broken, it seems to be weakened beyond the loss of men. The shortage so far of such units being ordered to resume the attack may be an indication of a commander's decision not to recommit these troops because of that weakened state.
Translating these ideas into rules terms, and specifically my Morschauser inspired HofT:
1) The test for heavy casualties that I instituted last year should be removed. It would be justifiable to have a test for a brigadier to order a unit taking fire to pull back but since I am not adverse to the player wearing multiple hats, it is unnecessary. A generic section on roleplaying subordinate commanders would be more apropos but someone else may write it,
2) Resolution of melee needs more thought. At present winning and losing is separate from consequences with weaker units (militia or shaken) being at risk of routing if they lose as well as being at greater risk of losing. Instead, the involuntary breaks should come during combat and the resolution result applied only to those survivors still under orders. So for example, instead of a shaken or militia quality unit taking more hits than it inflicts then failing a morale test and routing, it should simply be destroyed in the melee process, or at least take such heavy losses that the remainder are of no use. While there are good arguments for keeping broken stands on table from a simulation & moving diorama POV, from a gaming POV, I prefer to remove them and shall continue to do so.
3) Attack resolution needs to be at a higher level than the unit. Essentially all of the units of a command that are committed to a fight and survive need to be subject to the same result. Not quite sure yet how to work that but it shouldn't be too hard to define.
5) I need to reconsider the question of morale levels. I have been content with 2 which are measured by remaining stands, the idea being that when enough men have been killed, wounded, run away or are in a funk then the resolve of the remainder drop. Two states might be enough but it needs looking at as does the decision to base this on the brigade not the regiment. On the whole I am inclined to think my current approach is ok here.
Back to the books to look for those cases of defeated troops rallying and returning to the attack or counter attacking.