I’d like to suggest that the idea of reincarnation can be usefully framed as a metaphor.
“Whether you believe in God or not does not matter much, whether you believe in Buddha or not does not matter so much; as a Buddhist, whether you believe in reincarnation or not does not matter so much. You must lead a good life.”Dalai Lama
In every moment, the self we believed to be true dies, and another is reborn. This will continue ceaselessly until our bodies either physically perish, or until we transcend our self-identity and merge with the all.