There is no John Runnels listed in the roster of Battery H, 1st Illinois Light Artillery that I have access to.

Here is a thumbnail sketch on John Reynolds from Mineral, Illinois.

George Martin

John Reynolds

Residence Mineral IL;
Enlisted on 3/7/1862 as a Private.
On 3/7/1862 he mustered into "Battery H" Co. IL 1st Light Artillery
He was discharged for disability on 10/20/1862
Sources used by Historical Data Systems, Inc.:
- Illinois: Roster of Officers and Enlisted Men