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I have a '97 F350 with the E04D trans that I have the same question about. I'm chasing down a vibration. I haven't measured the amount but I would guess 2 mm. It's enough to make a clunking sound when pushing and pulling on it. That can't be normal. I'll post another question so hopefully one of us will get an answer.
I hope you still have your ears on. I did get my vibration fixed. I replaced the rear tail house bushing and the resulting play when pushed up and down and back and forth is a fraction of what it was. You don't get that clunking sound anymore as with the old one. Now you can see it move a hair but barely. Also, the new bushing came with some grooves cut into it like some main bearings have in a motor. It looks to be a much better design than the original. With the old one, after I removed it from the trans, I was able to twist it a good bit when I slid it over the driveshaft yoke. It was done! Anyways, it cost me about $25 for parts and a couple quarts of fluid and about four hours of time and viola......it's done!
Hope this helps! There seemed to be a lot of people having this problem but I only found one thread where the guy came back and posted his results. Good luck!
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