There were not any Southeast Block Island lighthouses made with rods.

I base this on the fact that Harbour Lights has stated several times that there are none.

Also Jim Rutherford in his Survival Guide states "While all the early Great Lakes Series had the lightning rods in their original design, only New London Ledge claimed one among the New England Series." Jim was referring to the 1992 Introductions of which half were the Great Lakes lighthouses and the second half were the New England Series.

I just got in touch with a person who has a single digit Southeast Block Island lighthouse, the number on his lighthouse is:
Number TWO
and
NOLightning Rod!!

Saint WackoPaul'
Keep the Flame

Onward to The Land of the Midnight Sun!