And thanks to the Dorset wills on ancestry and this website
http://www.opcdorset.org/Miscellaneous/DorsetNavalAdmons1696-1750.htm, I now know Thomas Plowman had another son.
Thomas Plowman junior was killed in a huge naval disaster on the Isles of Scilly on 22 October 1707 when four ships were wrecked due to a navigational error. 1,400 to 2,000 men were lost.
Thomas Plowman senior is here shown to be a Collar Maker and could sign his name.
What is very interesting about the link above is it shows the Plowmans in other naval administrations as well:
Surname of Deceased
WINDSOR Alexander
HMS "Eagle"
home parish: Winfrith Newburgh
Administra-tor/trix: Elizabeth, wife of Thomas PLOWMAN, mother
Sureties: Thomas PLOWMAN, collar maker of Winfrith Newburgh + William PLOWMAN senior, collar maker of Brianston
23 Jan 1705/6
DA/A/1705 20
PLOWMAN Thomas, junior
HMS "Eagle"
home parish: Winfrith Newburgh
Administra-tor/trix: Thomas PLOWMAN, collar maker of Winfrith Newburgh, father
Sureties: Administrator + Thomas HOMER, fellmonger of Wareham
18 Nov 1707
DA/A/1707 90
HOMER Thomas, junior
HMS "Eagle"
home parish: Wareham
Administra-tor/trix: Thomas HOMER, felmonger of Wareham, father
Sureties: Administrator + Thomas PLOWMAN, collar maker of Winfrith Newburgh
18 Nov 1707
DA/A/1707 73
So it would appear that Thomas Ploughman's wife Elizabeth had a child before her marriage presumably to a first husband and that he died in 1705/6 and was on the same ship HMS Eagle.
Then Thomas and Elizabeth's son was killed at sea in 1707 along with the son of Thomas Homer who was presumably a family friend or relative.
More digging to do...
Jon