Well, if all you want is a skirmish, then you can cover lots of places in this area. Cannon balls, all sorts of relics have been found all over Lonoke County.
What a lot of people do not realize is that what the Union called Brownsville was a rather large Union stronghold just east of Lonoke on Hwy 70. I have been told upwards of 30,000 people passed through there at Hicks Station headed some place. Iowa, Wisconsin, U. S. Colored Troops raised at Fort Smith, Illinois, were just some of the one who traveled through that one little spot.
One of your best bets is to just run a search on Google or some of the others.
You can read a certain book, but if general information is what you want, I would suggest you just start reading.
Brownsville was the county seat of Prairie County and was called an action by the Union troops.
Reed's Bridge near Jacksonville followed soon after on the way to Little Rock. The Union troops called it Bayou Metre, I believe.
The troops skirmished all over White County. If a man was killed there, then it almost had to have been some interaction between the sides.
You can pick up on a lot by simply reading the Union sites, especially in Illinois as they have a wonderful site.
Try reading all of the letters of Capt. Edward Eddington from Wisconsin
which I posted several days back. He speaks of the capture of Little Rock from a Union point starting before they enter the city.
Look at the recent posting on Thomas Barb's diary who was with the 1st Arkansas Cav. CSA He speaks of the fall of Little Rock from a Confederate point of view.
I feel sure that some folks like Doyle Taylor can add to my collection of
bits of information.
Good luck!