Push/Remote Start Honk Wire

Hey all, I need some help with wiring. I recently installed a push start system with smart entry in my Accord 8th Gen, the module has a negative wire that goes to horn to make it honk when car locks or unlocks. However, it only gives around negative 2-3 volts only to maybe honk the horn tiny bit but it still very loud so i was thinking to connect to a beeper/buzzer just like some new cars have but the issue is since the ground that comes out of that wire is only 3 volts the buzzer is not very loud. I thought a 4 pin relay would fix the issue as i used 12v positive + that 3v ground to power the relay and then 12v positive to pin 1 that should give 12v positive when relay clicks but still the pin 2 (output) is around 3 v max output. The other thing i tried was voltages step-up module but that doesn't work correctly either. Any idea on how i can convert that 3v ground wire to 12v ground to get full volume output from the beeper?Honda Accord

Not sure where you're getting "3v ground" or "12v ground". That negative output should be used as your ground for a relay or other low current (200mA or less) device. The +12v you need for your device should be coming from the battery positive with a fuse in-line.