The part I need is the small end of the setup you guys have pictured.
Bizarre, your picture shows the hose ending, with no valve end attachment, it is the bit at the small end I need.
vwmad, the picture you show is what I have exactly now. The barb of the valve end is still in the hose, but it is snapped off the actual threaded part that goes onto the air valve.
It must be common for them to snap with age and stuff going into the luggage compartment.