I used to install car alarms for a living and generally that gets connected to the parking light circuit which is a brown wire for GM cars. This brown wire comes out of the headlight switch and goes to the corners of the car and powers all parking lights. I've never worked on anything older than the 1970's though and I have gotten into the wiring on my firebird yet so it could be different for you. Sounds like maybe there's two circuits.

All you wanna do is mimic the light switch that's in your car. You don't have to run wire to each light, just power the wires coming off of the light switch. Toggle your light switch between parking lights on and parking lights off (not headlights on) and probe the wires coming out the back of it. One wire will show 12V then 0V then 12V then 0V as you're toggling the switch; just splice your wire in with this. If two different wires are toggling 12V / 0V then you have two circuits and you need to power both of them; if only one wire is toggling then only deal with that one wire. I don't know if 10A will be enough or not, you might wanna through a relay in there (I would).

As for the two circuits I think you can power both with this same signal. If there are two circuits, they both turn on and off at the same time and by the same light switch so you should be able to power them with the same signal (just put in one relay and power both circuits with it). Connecting them together won't change the net current flow so there shouldn't be an issue

you can also use this wire coming out of your alarm to honk your horn if you want