I'm intermittently hearing a knocking sound from the front on a cold start while in reverse. I do not hear it in park, neutral, or drive. I do not hear it when warmed up. Thoughts?

I was very reluctant to ever post this, And I will not be responsible for anyone acting on it. I fact, I was actually never going to post about it because no one else had ever mentioned it.

I had a very slight knock at start up I attributed to the toyota tic, probably isn't the ticky sound that they are actually talking about but I just wanted it out of my skull and so I quit thinking it about using some obscure excuse. My tiny little brain could picture the copper color showing through on my scored rod inserts.

I started doing a mid life refresh of the vehicle, changed my tranny fluid and have not heard it since. My fluid was 154,000 miles old and it was time. Simple drain and fill, 1st one of 2 planned.

Well that is my story, Could be I'm crazy, was a 60's kid, or I hit the sauce to much in Pattaya Beach, but I swear that it happened.
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What important to know is the knock timing keeping up with the RPMs of the engine, in time with the speed you're backing, does it knock in reverse and not moving?

In reverse both moving and stopped. I think it's in time to the vehicle speed not engine RPMs.

I may do that as well. I have to see when it was done if at all. I also have an exhaust leak tick, but that's separate from what I've been hearing recently.

2WD or 4WD?

I find your answer confusing, not sure how it could possibly be in time with vehicle speed if it does it while stopped.

Long shot, but I had something similar. Turned out to the the exhaust contacting the skid-plate, only in reverse. (Very close tolerance).

May not be a skid plate but may be something mechanical (exhaust hanger, heat-shield etc) somewhere along the exhaust line that makes contact when in reverse but not forward (As the engine rotates on the mounts one way or the other between them)

(An actual engine knock I would expect to act the same in either gear)

Im on my 3rd 4th Gen with a V8. And it has been a mystery about the tic, which after this video(https://youtu.be/96cpY2vb_n0) explained that the V8 has a weak make-do manifold. He shows 2 working solutions: Get a different brand manifold or try CRC Maniseal, which actually works. And be sure to run the car after putting it on. He mentioned the sulphur smell too.

Since it makes the noise when not moving, my thoughts are that it's either an exhaust leak or a motor mount.

Second thought is trans mount or as mentioned above, clearance with another part.