I think you've a mispelled name. This happens once in awhile. I was searching for a Kaufman but it turned out to be Hoffman. Unless you are absolutely sure it's Runnels I think it may be Reynolds. If the person taking the records misheard the person reading it it may have happened. In Bat H there is only one John with any name beginning with an "R" at that is Reynolds. Perhaps this is what happened:

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

ILLINOIS CIVIL WAR DETAIL REPORT
Name REYNOLDS, JOHN
Rank PVT Company H Unit 1 IL US L ART

Personal Characteristics
Residence MINERAL, BUREAU CO, IL Age 41 Height 5' 5 1/2 Hair LIGHT
Eyes BLUE Complexion FAIR Marital Status N/A Occupation MECHANIC
Nativity AMERICA

Service Record
Joined When MAR 7, 1862 Joined Where N/A
Joined By Whom N/A Period 3 YRS
Muster In N/A Muster In Where N/A
Muster In By Whom N/A Muster Out N/A
Muster Out Where N/A Muster Out By Whom N/A
Remarks DISCHARGED OCT 20, 1862 FOR DISABILITY

In all of the Union Army when I search John Runnels there is only twelve total and just one from Illinois but he was infantry.

John Runnels
Residence Charleston IL;
Enlisted on 12/2/1861 as a Corporal.
On 2/18/1862 he mustered into "G" Co. IL 54th Infantry
(date and method of discharge not given)

ILLINOIS CIVIL WAR DETAIL REPORT
Name RUNNELS, JOHN
Rank CPL Company G Unit 54 IL US INF

Personal Characteristics
Residence CHARLESTON, COLES CO, IL Age 21 Height 5' 5 Hair BLACK
Eyes BLACK Complexion DARK Marital Status SINGLE Occupation FARMER
Nativity RUSHVILLE, OH

Service Record
Joined When DEC 2, 1861 Joined Where COLES CO, IL
Joined By Whom CPT BELKNAP Period 3 YRS
Muster In FEB 18, 1862 Muster In Where JONESBORO, IL
Muster In By Whom N/A Muster Out N/A
Muster Out Where N/A Muster Out By Whom N/A
Remarks N/A