toggle relay with pwm output

Need some help on this. I was planned to toggle a relay by the Hi-beam, which is used for both hi-beam and DRL. When I using the DMM to measure the voltage, I found that the Hi-beam is either 12v (Hi) or 7.6v (DRL), and I thought that's going to be ok. But when I hope up the relay, when Hi turn on is ok, but when DRL on, the relay just buzzing and not turn on, so I guess the DRL actually is using PWM instead of just with lower voltage.

How can I solve this issue? I think a capacitor may help, will that work/ If so, how big of the capacitor I should use?

Thanks.

I added the capacitor to the diagram, will that work?