I did something similar in my '98 Wrangler. I actually have 6 strips spliced to my dome lights, so when I open up the doors, they light up. At first, I wanted to splice the wires (like you said) at the button where the door closes on, but instead I spliced it to the wire that led to my dome light on the roll bar. To be exact, there should be a bundle of wires on the roll bar that leads from the back of the driver's seat to the top of the roll bar where the dome light is. Well, at least for my TJ it is. Find the right wire and splice it together! Took about 15 minutes to wire up. Very easy and clean install!
'98 Jeep Wrangler 2.5L | 4" Pro Comp Lift | 33x12.5x15 Dunlop Mud Rovers | Two 10" Polk Audio Subwoofers | 2 Amps (800w Eclipse and Alpine MRP-1000 Mono) | Kenwood Head Unit | Ham Radio w/ Comet SBB-7 Antenna (Call Sign: KK4BUE) |CB Radio | Hella Vision Plus Conversion with 50w 6k HID bulbs | Lotta Lights |