Rendering multiple cameras

I'm working on a mech game and I want the main view to be 3rd person but in the top-right corner I want to have a camera first person view from the active weapon system (and cross-hair overlay).

I saw there was already a question about "picture in picture" and that it requires Unity Pro's RenderTarget but what if it's all from the same scene?

No, "Picture In Picture" doesn't require Unity Pro or render textures.

You can simply create a second camera in your scene, ensure that its "Depth" is higher than your main camera, and set the "Normalized Viewport Rect" settings to change where it is rendered within your game view.

You can just change the normalized rect for the second camera to 0.8, 0.8, 0.2, 0.2 or so, and that should show it at the top right, taking up 20% of the width and height

Note: you'll probably need to change the depth value for the second camera to be 1 higher than the main camera