Frank the roster for the 9th Cavalry Company L says he was from Newton not far from Marshalltown. I tried to find him in census records but so far not much luck. Do you have a wife's name or other children? Here is the roster entry:

Kimberly, William L. Age 18. Residence Newton, nativity Iowa. Enlisted Oct. 13, 1863.
Mustered Oct. 13, 1863. Mustered out Feb. 3, 1866, Little Rock, Ark.

He applied for a pension, and that might give you some family information. I'll try to find the pension certificate numbers and get back to you. Here is the date:

Name: Kimberly, William L. Date: 28-FEB-1907 State/arm Of Service: Iowa Cav. Company/regiment: L,9