So if you jump the F socket to another lit socket, the bulb does light.
Did you check one of the other Relays (C,D,E) with a volt meter
to see which terminal is the 6V, then checked the terminal in the
same position on the F Relay to see if it's pushing out 6V. If it is,
then a little jumping should narrow things down. If it's not, then something
in the box lost connection and you'll want to jump a wire to that F terminal's
circuit so it pushes out 6V.