Let me caveat by saying that I am a new homeowner with relatively little electrical experience, so please bear with me...
Our house has a standard 3-way switch with the light between the two switches. Originally I wanted to convert the 3-way to function as two single pole switches. I would have to add more wire directly between the switches to make that work, so I'm trying for a simpler option. Essentially, I want to splice an additional light onto the second switch, to work in tandem with the light in the middle. (see diagram)
The 3-way switch is working fine, but the new additional light turns on for a second and then off. First, does this setup work? If it does, does anyone have any ideas why the light is turning on then off immediately?