Actually, the visor was both inside and outside.  Huh?  That is, the upper cranium above the visor's "brim" protruded a skant few millimeters more outward than the lower "face" and jawline.  Thus while the visor retracted "inside" as it rose, when fully lowered, the lower edge covered a thin section of the lower "face".

On a side note, it is thought by several fans that the famous Cylon "scanning eye" was inspired by Gort's "laser vision".  No personnel from the original BSG has stated this in interviews, so it's really just supposition, but one can't deny the superficial resemblance between the two designs.

Sincerely,

Bill

Tempt the Hand of Fate and it'll give you the "finger"!