I don't know what information is listed in pension applications, but James Green Campbell's wife, Lucy M. Taylor Campbell did apply for a Confederate pension in LA.

Louisiana Secretary of State
Confederate Pension Applications Index Database
Selected Name Detailed Data

Reel: CP1.23 -- Microdex 4 -- Sequence 4
Target card: CAMPBELL, LUCY M.

Applicant Information & Name Variations:

CAMPBELL, LUCY M. (TAYLOR)
Parish: ST. LANDRY -- Pages: 2

Soldier Information & Variations:

CAMPBELL, JAMES G.
State: LA
Branch: CAVALRY
Unit: 2ND REGIMENT (33RD REGIMENT PARTISAN RANGERS)
Company: CO. A

Also, William Simpson Campbell's widow applied for a Confederate pension

Louisiana Secretary of State
Confederate Pension Application Index Database
Selected Name Detailed Data

Reel: CP1.23 -- Microdex: 3 -- Sequence: 20
Target Card: CAMPBELL, FANNY VIRGINIA

Applicant Information & Name Variations:
Name: CAMPBELL, FANNY VIRGINIA (TOBY)
Parish: ORLEANS
Page Count: 6

Soldier Information & Name Variations:
Name: CAMPBELL, W. S.
State: LA
Branch: CAVALRY
Unit: 2ND REGIMENT (33RD REGIMENT PARTISAN RANGERS)
Company: CO. A
(Above military data is from the War Department.)

Name: CAMPBELL, W. S.
Branch: NAVY
Unit: GUNBOAT, "PONCHATRAIN"

David