Here's a nice video of the prep and launch of the eventually fielded version with the rectangular fins. The pre-launch spinning comes from a simple wind-up spring mechanism. Betcha' didn't know that the Army likes its rockets painted pink! Actually, I'm sure it was painted red and the film's red dye component has faded over time:
https://www.youtube.com/watch?v=eL-g8iekmIU
Here's a description of the on-rail spin thing:
"Unlike the Honest John rocket system, where the spin is initiated by the
spin rockets after the round leaves the launcher, the Little John rocket is
stabilized by imparting spin to the rocket while on the launcher, just prior
to firing. This method of stabilization is known as the saucer concept,
'spin-on-straight-rail' (SOSR).
Prior to firing, a flat coil spring mounted under the rear of the launching
rail (fig 15) is wound 8½ complete turns. The spring is released when the
lanyard is pulled, turning a drive shaft which rotates a pinion gear meshed
with teeth of a ring gear attached to the rocket nozzle. When the rocket
reaches a spin rate of 3½ revolutions per second (rps), inertial switches
attached to two thermocell batteries close a relay and provide power for
activating the igniter for firing.
As the spinning rocket clears the rail, the front shoe is ejected and the
rear shoe retracts up within the fin barrel on the rear of the rocket. The fins
are canted to maintain this initial spin."
BTW, thanks for all of the on-line photo source suggestions but I'd already found all of those. Believe me, I spent a lot of time searching already. I was hoping someone might have personal photos from a museum visit like mine of the Nike missiles that are local to me.