Birth certificates did not exist at this time, so (usually) only the baptism was recorded
Sources
Devon Baptisms (database), transcription by Devon Family History Society
Parish baptism register (Plymouth Charles) via findmypast
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DNA Connections
It may be possible to confirm family relationships with Eliza by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Eliza: