Thank your for you help, Bryan. I don't know if you know the questions asked on the "Form A" of the app, but here is what said.
8. In what State was the command in which you served organized? Arkansas
9. How long did you serve? Give, if possible, the date of enlistment and discharge: About 4 years. I enlisted Oct 1861 and served to the surrender.
10. What was the letter of your company, number or name of battalion, regiment or battery? Company "E" 19th Arkansas Regiment.
11. If transferred from one command to another... was transfered in about June 1862 to Company "G" Brooks regiment, and served in that command until the end of the war.

Also included in the app is the letter requesting military records to the War Dept. Here, it states that he is reported to have in enlisted in Company E, Reginment 19th Arkansas Infantry. Below this is has Company G, 26th Arkansas Infantry.

Looking back over this, this is probably why the Pension was rejected. 1) they Pension dept was looking for Z.F. Elliott, when he was listed as Frank Elliott 2) he was in the 34th, not the 26th.

This is about the luck of my family! Thanks for you help.