At the end,
*** Spoiler - click to reveal ***after you drop Solidus, Raiden will be on the street talking to Snake. Pay attention, and don't skip over the part where Raiden looks at his dog tag. As he looks up, press R1 (FPV button) and look to the right of Snake (between Snake and Raiden). You will see Vamp in the distance.
Questions, corrections and neg vote justifications below.