Hello.
I re-found this post by accident and as I have my heater box out (total nightmare to do) I took some pictures. This rod couples to a small plastic piece (see below):
The purpose is to connect the heater hot-cold (heater matrix) unit that the grey Bowden cable connect to and moves the mechanism on the RHS of the hot-cold box to the flap control unit that directs the air to the vents. Sort of vent control. The articulation of vent controls is very complicated and a sheer work of genius.
Hope these pictures also help:
The plastic part that you’ve lost is also used on the top of the hot-cold (heater matrix) unit that the hot-cold cable links to, to regulate the temp.
Let me know if you need any further pictures, but sorry, I can’t find the part on my parts catalogue, which is strange.
HTH