'91 Integra + Varad ILK to domelight

I wanted to know if I did this right.  I connected a varad interior lighting kit to the door trigger/domelight of my '91 Integra.  When the doors are closed, it has 12V; when you open the doors it's negative.  

So I had to use this:

Then I used the 12v+ output of the first relay (converting negative to positive) to give 12v+ to the remote turn on lead of the second relay:

and then pin 30 going out to the varad ILK.

My question is: Did I need to use a second relay?  Should I have just used the 12v+ output on the first relay?

Please help, Thank you in advance for your time.