The following information is available on a quick search.

BOOTH (1920)
Olive, William, Sr., Pvt. Co. B, 2nd La. Cav. On Roll of Prisoners of War. Paroled at Natchitoches. La., June 8, 1865. Res. Natchitoches Par., La.
Olive, William, Jr., Pvt. Co. B. 2nd La. Cav. En. June 18, 1862, Natchitoches Par., La. Roll for Jan. and Feb., 1863. Present, Color Sergt., since Dec. 8, 1862. Roll for July and Aug., 1863, Present. On Roll of Prisoners of War, Paroled Natchitoches, La., June 8, 1865. Res, Natchitoches Par., La.

NATIONAL ARCHIVES – NARA CSR M320 (www.footnote.com)
There are 7 cards of records in NARA for the two Olivers. They are in one file and are mixed together. Two cards indicate Jr., two indicate Sr., and the other three with no indication seem to be 2 for Jr. and 1 for Sr. The info on the cards is the same as mentioned in Booth.

NPS CWSS - www.itd.nps.gov/cwss/regiments.cfm (M378 roll 22)
Both are listed as members of Co B, 2nd LA Cavalry-CSA

With Olive Jr. being Color Sgt., it is surprising that he wasn't listed as being captured at Henderson Hill on March 21, 1864. The Regimental flag was captured by Wm Ayers of the 35th Iowa. As mentioned in a recent LA Msg Bd note, the 2nd LA Regimental flag was up for auction last Friday, being sold by the Southern Oregon Historical Society to raise money. The two Olives were either not there, they were among the few troopers who managed to escape, or they were detailed elsewhere (away from the main body of troopers).

Do you have any pictures or relics / mementos that belonged to Sr or Jr, or know any more specific details about them? If so, I would like to know what. I had at least 8 family ancestors in the 2nd (Co E and D) and might find some helpful information from your info.

Hope this helps

Don Parker