Stevenson started with a belief he inherited from his mother and then spent the rest of his life gathering anecdotes that he could use to confirm it.
As Michael Shermer said, "Smart people believe weird things because they are skilled at defending beliefs they arrived at for non-smart reasons."
Stevenson began with the risible belief that some illness cannot be explained by genes or infection but only by reference to past lives. Similarily he postulated that birth marks and defects are signs of wounds sufferd in previous lifetimes.
Not surprisingly he went to India and other countries where belief in reincarnation was already rife and started interviewing children via biased interpreters. Children in these cultures are raised from infancy to believe they have lived many times before and no doubt entertain childish fantasies about their past.
Interestingly when children talk about their past lives they are almost always of a higher class and lived and died in dramatic circumstances.
Stevenson's work was entirely unscientific. Nothing could possibly be allowed to count against his beliefs. Any time a child's story didn't check out it was simply discarded. Any time he found a connection between what a child said and some historical reality, however tenuous, it was marked up as evidence.
Stevenson never proposed any mechanism for how injuries experienced in one life could physically impact on the next. He only cared about collcting anecdotes like an obsessive train-spotter collecting locomotive numbers.
What a waste of a mind. The only empirical experiment he ever did was the day of his death. So far he hasn't bothered to report the results.