I have to get rid of that lousy junction box

There is an old junction box in the laundry room that is related to a bad circuit my electrician refused to fix. If I disconnect anything, it causes a free neutral and makes the lights blink. Today, I start to trace the wiring to see if I can figure out the problem myself. I start opening up every wall plate in the house, running tests, and making a map.

A junction box with one outlet installed in a finished wall.