I'm trying to understand why a switch loop in my house was wired in this manner and if I need to correct it. I'm assuming it is incorrect because I cannot turn the light off and on from both switches. I included a diagram of the current wiring I can see and pictures of the switch receptacles. I'd like to avoid running new Romex if possible. The source comes into the light socket via the attic (Black and White only,) down to the first switch, and down to the second switch. Black, White, and Red wires are present with no ground between the switches.
My plan was to swap the bulb out with a recessed light fixture. I'd love to be able to add a smart switch in eventually, but it's not a dealbreaker. I need to hook up the light as well so guidance on that would be appreciated! Thanks!
First (Left Switch)
Second (Right Switch)
This is within the first switch box.
To First Switch (Left in Diagram)