My restoration project - 2005 Jeep TJ & my steering wheel vibration

Have you tried just changing the front wheels with the rear wheels to see if you have a wheel or tire issue. I experienced a similar problem after replacing winter tire/wheels by summer tire/wheels and doing a tire rotation at the same time. One of my front tire/wheel was the cause of the steering vibration.
there maybe some truth to your words. I found out that my back right rim is a little crooked and the rest 3 tires are not evenly worn out.

no boundaries no borders - wrangler
 
JMT i checked the tires and the rims. I found out that my back right rim is a little crooked and the rest 3 tires are not evenly worn out. Ill keep that in mind and maybe is my next move after the track bar

no boundaries no borders - wrangler
Trackbar bushings at the axle side could be worn out, not uncommon, or the mounting hole worn out into an oval shape. Either way, that is a problem spot. 90% of death wobble happens because of that spot. It is most commonly set off by the tires being out of balance or a rim bent (which would cause out of balance and make it very difficult to balance). I would check the other things like trackbar, hubs, ball joints, upper and lower control arm bushings, etc...just for good measure, but it still sounds like tires (and now rims too). Our TJ's are very sensitive to wheel balance. Just research precession and you'll see why. That solid axle is like two gyroscopes fighting one another. It's remarkable we can even drive them.
 
updating with he latest..
new radio/mp3 installed
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no boundaries no borders - wrangler
 
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That passenger airbag switch is interesting. I don't think we got those here in the U.S. I've got a spot where mine should be on my Rubicon, but it's just blank.
 
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That passenger airbag switch is interesting. I don't think we got those here in the U.S. I've got a spot where mine should be on my Rubicon, but it's just blank.
Oh I thought it was standard for all wranglers

no boundaries no borders - wrangler
 
After changing a lot of things with no results (bushings, suspension, steering wheel suspension etc) it was finally time to change my tires because they where old. When I changed my tires i asked from the guys to send my rims for checking if they are crooked or have any other issues. When my rims came back the guy told me that there was a lot of salt (for entering the wheels a lot in the sea water) stack to my rims between the disc brake and the rim creating almost a thick layer. It was really hard to remove it from the rims as it was almost part of the metal!! After cleaning the rims my TJ now rides smoothly and finally with any steering wheel vibration
 
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