I am new to RAM, but wiring is wiring.
I read through the install instructions, they say to use a rely, exactly why I am not sure, LEDs do not usually draw a large amount of current BUT, since they say to use it then be safe and use a rely. The only problem I can see is where they tell you to connect pin 30 and pin 86 to a constant power source.
To me I would run pin 30 to a power source and add a minimum value in-line fuse, then wire Pin 86 to an activation source, i.e. a switched power wire and pin 85 to ground. Pin 87 goes to the load (LED Lights).
NOTE: The FUSE on pin 30... check what they call out for a fuse, drop the value of that fuse by half, check out if it works (doesn't blow out), if it does blow out raise the value of the fuse until you find one that lives, trying to keep the fuse value as small as possible and then switch to a fast-blow fuse of the same value. (Sometimes a fast-blow fuse doesn't work out, if it does you are that much safer).
The next thing to check, the manual calls out using the Interior Light wiring to activate the Courtesy Lights, OEM wiring can sometimes be minimum at best, it will carry the current needed but easily overloaded. Make sure the wiring you tap is capable of carrying the total current load of both the interior lights and the new lights.
Sounds like a PITA but once you have a fused power line that works, fused as close to the power source as possible, and the proper wire size, the fuse will will cut off the power source as fast as there is a current increase and the wiring shouldn't get hot.
This is only a suggestion but the way I would go about it, thinking about possible problems you have raised.
Sorry if I went little too far.
Also, take into account I don't know exactly which lights you have, so tread lightly until you know what the needs are.
