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I completed the fluid change with Valvoline fully synthetic 75W-140 gear oil that already has a friction modifier in it. (I bought Ford friction modifier just in case.) The fill plug is a PITA to utilize as a filling spot. I could barely get 3 quarts in the rear differential even though it calls for 3.5 quarts. I took it for a spin and didn't notice any vibes upon turning take-offs, both left and right. Then we went to buy our horse trailer and I purposely did multiple turning take-offs. We noticed vibes when executing a left turning take-off after driving around for a bit. I'm guessing it took a bit for the fluid to warm up? I couldn't get it to vibe on a right turning take-off.
Should I add an ounce or two of the Ford friction modifier? Should I also try to add the other half quart of the diff fluid per the specs? Why would the rear end vibe only during a left turning take-off and not a right?