Hi there Steve,
Uncle Chris here, great minds must think alike or it runs in the family however distant the relationship. I too have been thinking about this family this afternoon.
Joseph Taggart was born 1833 therefore his father Andrew was born around 1808. This means Andrew's father was born about 1783. This piece of information may not appear to make life much easier but there is a chance that Joseph named one of his sons after his grandfather. I do not know about you Steve but I have a gut feeling about baby Vincent. I feel that whilst he only lived four months he may well play a fairly large role in helping us solve the riddle of the Taggart family.
All the Best, Chris