Kenneth, There is one Arthur Jackson in the Social Security Death Index, whose birthdate matches your father's: Arthur Jacksonborn: 14 September 1900died: March of 1967last place of residence: Le Roy, Mclean County, IllinoisSocial Security number: 348-38-8407 Social Security number issued in Illinois in 1963.
I would advise contacting: Lexington Genealogical & Historical Society Inc. (THE FORT) 318 W. Main Street Lexington, Ill 61753 Tel: 309-365-4591
Tuesday through Saturday 9 - 4
Try calling them during their hours of operation. Tell them you are seeking information regarding your father, whom you never were able to know. They have a wonderful card index with a card for every headstone in the county. Attached to this is a reference to the obituary if one exists for that person. They may be able to help you further, as many of the people who volunteer at the Fort are older and may have even known this Arthur Jackson.
One thing that would really help you in your search, would be to try to find the marriage record for your parents. If you have an idea which county they married in, write to the county clerk and order a copy of the record. There should be information regarding Arthur's parents, birthplace, etc. on the record. That would help you to determine if you have the right Arthur Jackson when you find a person of the same name, such as the one in Mclean County. His birthdate matches what you were told, but without other information, how can you determine if he is the right man, or not? If you don't know which county to begin looking in, start with the county your mother was a resident of, or where her parents lived.