Actually, that's a fair point, can't see the wood for the trees.
If the dining light is fed from that single on its own in the kitchen rose / JB, then it would not work... with a continuity tester, you could
The other thing I've noticed is that your diagram of the dining switch has the conductors connected to L1 & L2.
If this is the case, the switch will not feed a supply to the light fitting.
Looking at the wires you have, it seems possible that the live/earth feed comes to the switch from a ceiling point.
With a continuity tester (and power to the circuit OFF), you could try shorting the red and earth of that wire on its own in the kitchen rose / JB together and then seeing if one of the red/earth cables at the dining switch shows a positive reading.