Perpendicular Cut & Join Stroke using AG

[MahaB82A]

I want to have a perpendicular cut of black stroke of this portion in yellow color.

I separated stroke & fill & used "Perpendicular Line Tool" of AG & native Pathfinder tool. But it did not work. How to fix this? File was uploaded as well.

Perpendicular Cut

[Monika Gause · Accepted solution]

The stroke is already outlined.

Pathfinder Divide could work, but will only when there is 100% precision. I have used the shapebuilder tool

https://youtu.be/zo_RiP-AHs0

[MahaB82A]

How to join this gap using AG? File is uploaded

Join