Plugging away at this...possibly Argyle was in the Enrolled Missouri Militia. This would account for him not showing up in some soldiers databases. The Skirmish at Florida, Mo. on 22 July 1862 or Santa Fe/Botts Bluff on 24 July 1862 could have been when flag-bearer Jack Richards was killed. Both occurred on the Salt River. EMM would have been just a few days old and this would have had to have been one of the very earliest unit enrolled. These guys were just tossed into these reserve-type units with little fanfare and there is anecdotal reports from some who served in them that they didn't know the designations of their units or even consider themselves "in the army." And Argyle's father could easily have been in a different EMM regiment.
If Harvey Argyle was in the EMM it likely would have been a unit raised around Audrain County or an close adjoining county.