Ignition Fuse Blowing After Alarm Install

Shouldn't ever bump up fuse values to try to fix the problem; that defeats the purpose of the fuse, risky- So are you using the (+) output for the parking lights? You should check each side of the connection separately to isolate the problem- Put a test light on your alarm's parking light output and make sure it lights up as you expect when you activate the alarm; basically substitute the test light for the car's parking light connection. Though you're positive you have the right wire, check it again by measuring the voltage at the spot you tapped in for the parking lights, and see if goes high and low when you turn the lights on and off manually. If it looks okay, you could try applying power using a fused wire to the connection and see if the lights come on- If they work normally that way, see if you can measure the current to see if it's a direct connection to the parking light circuit or maybe relay controlled. Are you getting the alarm power from a independent line from the battery or are you tapping in at the harness somewhere? If everything works in the tests above, the difference is the amount of load between the test light and the parking lights, and maybe that's a factor-