The only illumination for the high beam side of the SPDT switch would be a dependent illumination right? Meaning it depends on the switch being on to light up, and isn’t wired to something like the parking circuit.
Reason I ask is because that’s how it should be, but if you somehow got a way to wire the illumination to the parking lamps, you might have some feed in the switch backfeeding the high beam circuit, which is then barely illuminating the headlights on high beam mode through the MFS.
You for sure have the relay wired correctly for what you’re trying to do, I can confirm that much. I assuming something with your switch is the problem but I need to know more about what all is actually hooked to the switch. Ground for the illumination? Illumination power comes from where? Etc.