Believe this may be your man.
Joseph Rutledge Finegan
Residence was not listed;
Enlisted on 7/8/1861 at Fernandina, FL as a Private.
On 7/8/1861 he mustered into "D" Co. FL 2nd Infantry
He was Dropped on 9/1/1861
(Estimated date of being dropped)
On 3/1/1862 he mustered into "I" Co. FL 2nd Cavalry
(date and method of discharge not given)
* 3rd Sergt 3/1/1862 (As of Co. I 2nd FL Cav)
born in 1844
died in 1871
Buried: Duval County, FL