Thompson #2...

In a prisoner statement from Gratiot, Pvt. William H Adams reports being recruited by Porter August 1862 into Mill's company of Porter's Regt., but had served before in "Thompson's Company" now Pollard's joined for 6 months service. He reports fighting at Kirksville, Walnut Branch and specifically at Elk Fork with Thompson.

So I think Walnut Branch is the skirmish at Black Walnut Creek near Sedalia MO Nov 29, 1861
and Elk Fork I believe is in Pettis County with a contact with a scouting patrol in late April 1862. This in Volume 13, Chapter 25 - Operations in Missouri, Arkansas, Kansas, the Indian Territory, and the Department of the Northwest, pg 63-64. Or Elk Fork may be reference to the skirmishing pursuit of Porter from Paris which culminated in the action at Kirksville as described ibid. Pg 212.

Pollard referred to is Capt Braxton Pollard of Marion County of the 1st NE MO Cav. Pollard's unit was known to be with Porter at Moore's Mill, Paris, and Kirksville. So to get a little closer to who Joe Thompson was, it appears he was a predecessor to Pollard in the 1st NE MO Cav. Pollard never received a company letter designation but the majority of his men came from Marion and Ralls Co.

Scrounging in the rosters of NE MO Cav I find one 2nd Lt John S Thompson of Franklin's Regt. 2nd NE MO Regt Cav. He becomes the Captain commanding Co B 2nd MO Cav. He resigns his commission 24 June 1864 stating he was old (48), just a farmer and had no formal training in drill or military tactics.