I have been following this thread with interest, admittedly amazed that for all the trees and ink sacrificed over the decades on the relatively and enduringly famous subject of the "thin red line" (to sustain an erroneous quotation!!), that so little is actually documented or truly known about it usage.
But, I offer what might be one glimpse of the true thread of usage I came across just the other day. Perhaps it owes its appearance in print only because its context was an examination of an alternative drill offered by another "fertile genius" to cope with perceived deficiencies.
“In America, it has been the practice to adopt the formation of two deep; but as troops may be employed in different countries and situations, we should have an establishment calculated accordingly ; whenever the depth of our Battalions is reduced, the extent must be increased, and the Column of March being lengthened considerably, the movement of great bodies becomes more difficult ; besides, in an open country, the fire of three ranks must give a manifest superiority over the feeble efforts of two ranks.
“The system of formation I have here established is three deep, conformably with the European School ; the hint is taken form the Memoirs Militaires de Guischardt, Preface du Traducteur sur la Tactique d’Arrien, Tom, 2de P. 111. It is calculated principally for an open country, and supposed to be the most perfect arrangement for troops armed as we are at present ; but to act in an inclosed, woody or mountainous country, it may be not only necessary to reduce the formation to two deep, or even to one rank, but to open the order considerably ; for as irregular fortification is to regular, so is this irregular kind of formation, to that of three deep, the primitive and supposed most perfect arrangement ; whenever the country permits the use of the primitive formations, it is to be preferred ; but in situations where a change may be necessary, it must be left to the genius and skill of those who command.”
From Dalrymple, William, Lieutenant-Colonel. "acticks. By Lieutenant Colonel William Dalrymple, of the Queen's Royal Regiment of Foot," Dublin, 1782; pp.ix-x.
It strikes me as evidence for the conceptual opening for those like Wellington, who chose two ranks rather than three, whatever Dundas might have had to say on the point, six years later :o)
Regards - Howie