The guy who died in 1654 was in Hartford, CT so maybe that's who he's supposed to be. That John Hopkins (who married Jane UNK) arrived in MA in 1634. See the best source for him:
"John Hopkins of Cambridge, Massachusetts, 1634, and Some of His Descendants" (1932, Stanford Univ. Press).
He's not son of Mayflower Hopkins or either wife. He wasn't the son of Mary because she died in May 1613. He wasn't the son of 2nd wife Elizbeth because they married in 1617. John (and a mythical Stephen and Wiilliam) were assigned as sons of Stephen by various people in old books because they wanted a Mayflower connection. Some also have them as the sons of the mythical Constance Dudley who we know was an error from the beginning since there never was any record for her. She was disproved in 1998.
There is a bapt rec for a John Hopkins for 14 April 1611 in London with father listed as Stephen Hopkins, but that won't work for Stephen of the Mayflower because he hadn't been in England for a couple of years. But there are 14 other John's just in London with baptism between 1600-1620. But that's just London. We don't know the birth date or place for John of Hartford.