Sue: I looked under many variations of spelling and could not a Civil War listing for Jordan, Jerdan, Gerdan Pearce.
However, I also looked through the census records that are available on the internet.
The 1920 census for Boney, Curry Co., New Mexico lists: Jordan Pearce, age 62, his wife Emma, age 65 and "Mother", age 81. It also shows that Pearce's father was born in Texas and his mother in Georgia. Wife's parents were from Georgia.
This means that Jordan was far too young to have entered the Mexican or Civil War. If he were living in New Mexico during 1877, he may have belonged to the New Mexico Cavalry. I believe there is something listed on the internet about a New Mexico Regiment. I'll let you know if I can locate it.
Sorry I could not be of more help. At least you know that Jordan was living in June of 1920. Marrows timeframe a bit.