This video shows the experimental third person view in the latest version of the MelPyth mod, M5. You'll see it definitely isn't perfect, but hopefully it'll give you a sense of how such a view could work. I should mention the controls: in this mode (FLOATINGCAMERA), the movement keys move both the player model AND the camera. This is actually a big problem in getting the the view right as well as getting the model to move where you want it. It's not like there's a fixed camera position behind the character. Looking around simply turns the model. Your weapons will fire in the direction that the camera, not the player model, is facing. So if the camera is looking towards a tunnel it doesn't matter where the player model is looking because any shot fired will go to the tunnel. It's an ultimately impractical mode the way it's coded now, but I suspect it was never finished.
A million thanks to Melanikus for making this available!
This video was recorded with Fraps on a 2004 Dell computer. To get this mod to work properly, you will need an old computer with AvP Gold on it. You can technically install it to your AvP Classic folder but you'll only be able to experiment with the Image Intensifier on because of a graphical incompatibility with newer graphics cards and the old version of DirectX.
The MelPyth mod was made by astro_muppet and Melanikus. M5 dates to 2007 and is available here: Indiedb.com