The United States has been in wars besides the American Revolution, the War of 1812, the Civil War and the two World Wars. Is it possible that your ancestor served in one of the Indian wars, the Spanish-American War, or the Philippine-American War? Involvement in any of those actions would have generated service and possibly pension records.
If your genealogy “problem” is during a period when railroads were in operation, do you know where the nearest train station was for your ancestor? Do you know nearby stops along the way? People could hop a train to elope, look for work, or simply leave home and never come back.
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