The circuit is through the contacts on the key cylinder and the surrounding section of the column.
Take a look at the area that I have placed the tape on.
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I have done that to all my vehicles to stop the "Key in Ignition Chime".
you may need to remove the key cylinder and clean the contacts inside the column.

 

I suspect that little red-tipped contact is the culprit. When you insert the key, the key forces a small bar in the moving part of the cylinder to slide out of a square hole and push that red tip out, moving the long skinny contact out and making the connection. When the key is removed, the bar slides back in, allowing the red tip to fall into the hole, allowing the long contact to break the connection. I was messing with a brand new cylinder today before installing it, and messed that contact up. I bent it so it "looked right" (I thought), and now my chime is always on if the door's open, key or no key. I think I bent too much curve into it, so that even when the tip falls into the hole, the middle of the contact (where the little bump is, even with the upper fingertip) is still pushed too far out to break the connection. I'll be back to confirm this after I try and bend it flatten to fix it.

Well I failed to remedy the problem, but I'm still confident that contact is where the problem lies. I just couldn't get it back to the shape it came in.

 

Our door chime does the same thing. it seems to stop (with key removed) when you slightly wiggle the turn signal stalk. Still, a permanent fix would be nice.

 

I just put in a new cylinder and mine started this. I'm leaning toward the disconnect option.

 

Where is the door chime? I just want to remove it. My truck is a 2014 e350.

 

Timely revival of a zombie thread. My daughter's 2005 F-150 is doing the same thing.

 

I have a '97 4.6 with the same problem. It happens intermittently but usually stops by jiggling the ignition.

 

Most likely cause is the contact for the key chime that clips onto the column at the lock cylinder. It has 2 plastic tabs that hold it in place and when they break the contact grounds against the column. The contact is part of the clockspring harness and the only way to get it is get the clockspring. I fixed mine with some super glue and a ziptie.

 

I removed the steering column shroud and found the contact on the dumb dumb wire was bent. So I went snip snip and no more door chime. Best part is it still works if you leave the headlights on.