Thanks to my.is member dasgalloway for this picture and sophiesleeps for the original tutorial this was based off of.
In one simple picture.
SophieSleeps had posted this a while back with wiring diagrams, thought I'd follow up with a picture since I fixed one today. To confirm, all we did was cut/tap 1 wire to another.
Image shows what to do to fix a P0161 CEL on a 2002+ Is300.
To fix a P0141 (B1S2 Heater malfunction), all you have to do is switch which wire is cut and which is tapped, so instead of cutting red and tapping to green, you cut green and tap to red.