2005 Mercury Mountaineer,Reverse band broken no reverse

SOURCE: 2005 Mercury Mountaineer shuts off

Could be a number of things and the information is a little vague. Does it do it when cold, warm, after driving for a distance etc. It might pay to have some one run a diagnostic machine on it. The cost for the test could actually save you money. Just make sure they have a good reputation.

SOURCE: why are my reverse lights staying on in all gears - 00 cougar

usually located at shift linkage on transmission

SOURCE: In 97 mercury mountaineer, how to turn off "check engine" light

Go to the local parts store, have them check the codes (they will do this for free usually). It will tell you what sensor needs to be checked/replaced. Once the part is replaced, it will clear on its own. They can also reset the code, but it will come back if the trouble persists.

SOURCE: 2005 Mercury Mountaineer rear end whine, how hard to fix

Before you do this you might want to try fresh gear lube. On Ford products they use a synthetic additive in the rear and not in the front 4x4 axle.
The next thing would be to determine if it is a wheel bearing or a pinion bearing. You have to pull the axles and eliminate them as the problem. You might get lucky and not need to do the pinion.
The technical part of shimming the pinion gears with replacing the pinion bearing is about the worst part of the job. You won't know about the gears until you see them. You will need extra shims on hand.
It is a moderate job for two people. If you have all the parts it can be done in a day.

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SOURCE: I have a 2004 Mercury Mountaineer. Sometimes when

you probably should change the transmission fluid and filter with that many miles on it.