I took the tack of assuming he didn't leave Massachusetts, since I know little about Virginia records.
I've added to his profile the little that's in the Mayflower Families 5 Generations on Hopkins. It suggests the possibility that William removed to Medfield, Mass., and with wife Deborah had 3 children. I found evidence of a fourth, and Deborah's burial is out in western Massachusetts. So, if William of Eastham is the same as William of Medfield, he probably died by, say, the 1760s. Deborah's daughters married in Mass., and appear to have remained there. It does not appear that Deborah married a second time.
I found no evidence of a death record, will or probate file for William Higgins. The one probate file I did find, in Suffolk Co. 1758, was not his, but for an (apparent) unmarried mariner in Boston.