Headlight issue

I own a 1996 toyota supra which has two sets of dim lights. The outer set doesnt come on when I turn on my headlights. These lights are supposed to come on with the dims then turn off when the high beam is switched on. I checked the bulbs and that wasnt the problem. Someone also wired a turbo timer into the relay for the fog lights, and I tried un-plugging that connection to see if that relay was the issue. When I put the relay in its place the lights still didnt work. How can I fix this issue so the lights come on?

the included picture shows the headlight, the smallest one is the issue here.