Julian;
Of the two white wires departing the F3, one supplies the front Parking Lights, the other supplies the rears AND Instrument variable lighting by way of pin 4 of the six pin connector under the dashboard.
As a rule, wires do not develop breaks on their own and without external insult...connection problems typically occur at corrosion or looseness at terminations (fuse holder, connectors etc.) ...so look there first...try reseating the six pin connector under dashboard! Apply ACZP!
Reference:
http://www.sw-em.com/122S%20Wiring%20Diagram.jpg
ACZP:
http://www.sw-em.com/anti_corrosive_paste.htm
Good Hunting!