From the diagram, the only difference between low and high is the dip/full switch, at the left of the combination switch block.
Is there voltage on pin 6 when the headlights are on, high beam?
I would check for loose or corroded connections & broken wires before doing any modifications.
If there is voltage on pin 6 (with the meter negative on a chassis screw or clean metal), does that go to near 0V when you select low beam. If it does and the low beam does not come on, the fault is external to the switch. If the voltage stays around 12V, the fault would appear to be within the switch.
Just linking pin 6 to 7(?) is not a good idea, as the headlamp flash switch (2nd section of the combi switch) will ground that through the diode, which is only intended to carry the relay coil current. The actual lamp current is much higher - it will almost certainly blow that diode, and may wreck the switch if the contacts and internal connections are not big enough.