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The 2001 and newer model TJs also use a hybrid flasher circuit just like the pre-2001 models. However, DC decided that the previous design needed a change and so the IC chip in the flasher was swapped to a different (but similar) model. This rendered the previous flasher mod as null and void.
NOTE: If you want a drop in replacement flasher, with no modifications necessary by you, then you will want to to see this new flasher available from Mark Lochridge of Gold Coast Distributing Co.
If you wish to attempt a modification to your factory flasher, continue reading this write-up. Many thanks to Jeepin' Geo on JU for the pics and information. He was very supportive in allowing me to post the pics and info here so as to provide the readers with info for the newer TJs.
Here is the location of the flasher relay in the 2001 and newer vehicles. Note that it is now located on top of the steering column instead of below it as in the older models.
Since I have not taken this version of the flasher apart, I will assume that its case is held on in the same manner as the older model. If so, then there are three tabs on the bottom of the flasher that holds the guts inside the shell. Use a small screwdriver to pry the tabs away from the body of the flasher so that the insides can slide out of the case.
Unlike the earlier models, this flasher's lamp out detector circuit can not be bypassed by simply cutting the circuit run. Instead, you must install a small relay which effectively bypasses this part of the circuit and allows the flasher to function at the normal (and desired) flashing rate. The relay can be obtained from Radio Shaft, part # 275-241. It is small enough to fit piggy back in the flasher module and you will be reinstall the cover once you are done.
To make all of this happen, you will need to be comfortable with a soldering iron....and I don't mean one of those big 3000 watt flame throwers that I've seen some folks claim are soldering irons (yeah, right!). It you are outside of your comfort zone at this point, then I suggest you find a friend who can do this for you. It is not overly difficult, but there is no reason to burn up a perfectly good flasher while you attempt to learn how to solder.
To make things a bit easier to see, the flasher relay was removed from the module in this picture. You should not have to do this in order to make the 3 wiring connection to the circuit board. Note that there is also one jumper connection on the Radio Shack relay itself, between one of the coil contacts and the ground pin. Don't forget to do this one too or else you won't get the results you are expecting.
Here is the complete flasher module with the flasher relay back in place AND the Radio Shack relay that has been connected via the red wires. Once the Radio Shack relay has been installed, slip the flasher module back into its socket and try it out (I would probably not put the module cover back into place until I've had a chance to test the flasher module in the Jeep....just be careful when you test it and make sure it does not touch anything while the cover is removed).
When everything checks out OK, reinstall the cover, put the flasher module back into the socket, and test it one more time. If all is still a go, then put the dash back together and wrap up the project. You are good to go at this point.
I hope you enjoy your new LED tail lights as well as your flasher mod.