This is like Deja Vu all over again!
I have been on this page a few times over the years.
Is this a Base Model 2003 KJ or "except base"?
How much current are you measuring?
You expect to draw about 30-40 milli amps ie 0.030 Amps!
First plug everything back in place.
Then assuming you have the 2003 Jeep KJ Service Manual go to page 8W-12-29.
Put your Multi Meter on DC Amps and put it in series with fuse #34 15 A.
Check Radio is Off and all internal lamps are Off...make sure doors are closed while you do your measuring.
You will see on page 8W-12-29 that there are a whole lot of lamps...unless you have a Base model.... at the bottom of the page on the Pink Wire coming off pin 18 on connector C2 of the Junction Block ie. Fuse Panel.
This Pink wire goes through Connector C306 and then C308.
Hopefully you will find the physical location of these two connectors in the index of Section 8W under Component Locations.
First pull of connectors C1, C2 and C3 off the Junction block...this isolates everything except the BCM...hopefully the BCM is not drawing the current!
Put those connectors back in place.
Disconnect C306 and see if the current draw dies down.
Then disconnect C308 in case that section of wiring between the two connectors is shorting to ground somewhere.
This should isolate if there is a short in the path to any of these lamps or if a lamp socket is shorting out.
Then that leaves you with the Left and Right Courtesy Lamps, Siren if you have one, Radio and instrument Cluster.
You will then have to isolate each of these last items to see what is drawing current.
The Instrument Cluster has a single plug at its rear...try disconnect that.
If at this stage the BCM is not drawing current and C306/308 makes no difference and disconnecting the Radio, BCM, Lamps etc. makes no difference then one of the Pink wires coming off the Junction block may be shorting to ground somewhere so you need plug the connectors back in place and then cut off these 6 Pink wires, one at a time, as they exit the connectors C1, C2, C3. You can solder the wires back together later and insulate them with Shrink Tubing.
If cutting all these wires makes no difference to the current draw then it would point to the BCM.
I hope it is not the BCM Module that is at fault as that is plugged directly on to the Junction block ie. the BCM is on the reverse-side of the interior fuse panel!.....very hard to get access to!
You can download the 2003 Jeep KJ Service Manual here:
www.colorado4wheel.com/manuals/Jeep/KJ/