problem adding leds to alarm

Hi forum! I am trying to add LEDs to an alarm, 2 new ones in addition to the original one. I tapped into the wires for the original LED(12v), and added a few feet of wire and two additional LEDs(12v also). The LEDs I added work great as wired, however adding even one or both makes all of the LEDs blink twice as fast. This is not a problem and is ok with me.

However, with the new LEDs connected, All of the LEDs continue lighting after I disarm the Alarm.

In fact when I disarm, they go from a fast blink to an almost always-on-frantic- flash.  When I disconnect the new LEDs everything functions as normal.

If it makes a difference, the application is a ford explorer factory antitheft system. I have added a glassbreak sensor, and hoped to add a LED on each front door sill. I tapped into the theft light circuit of the cluster, which pulses 12v to its LED when armed.

I thought of trying the same idea but with a relay, or a transistor then a relay, but I dont know why the lights continue to flash now with the additional LEDs connected,

Thanks for reading this and for your help, I dont know enough about electronics to figure this out on my own, and i thought Id ask here before trying a relay and having the same issue.