The Camera's meter is a bit 'dumb'. It works on the principle that 'on average' a scene is gong to be 'about' 18% grey; so if you take a picture of a black cat in a coal hole, it will try and brighten that predominantly 'black' scene to something mid-grey, or wicky-worky, try take a picture of a white rabbit on a ski-slope, it will try and dim that very bright scene down to something similarly mid-grey.
You have a subject on a light-box. It would be usual then to assume that the cameras metering would likely try and 'dim' that scene,like white rabbit on a ski-slope, as overall its pretty bright.
However, the subject itself is infront of the light... that's the bit you really want properly exposed... but how well lit is it?
Turn the light-box 'off'. Try taking a photo, what do you get? Without any other light source, it's probably pretty dark, and the subject probably isn't 'lit' at all. Camera would likely try and up the exposure HUGELY to get that subject in acceptable detail. Turn the light-box on, and the back-ground is much better lit, but the subject itself, probably isn't unless some of the back-ground light is being bounced back onto the subject by the ceiling or something.
Ie you have two problems. First, basic metering principles, second strong back-lighting.
This is NOT a matter of 'settings'.
First up, you need to much better get to grips with manual mode,and making your own aperture/shutter settings. The strong back-lighting is 'fooling' in camera metering, it cannot be relied on.
You will probably want an aperture that will give you enough DoF to get the subject in focus, which at such short camera to subject ranges could be pretty shallow.
Shutter-speed, can probably be stretched to whatever you like / need, if you use a tripod and remote release, as I wouldn't expect your broach (or whatever) to be moving.
NOW, you need to light the subject.. that, ultimately is the important bit to expose 'right', and you will probably want to light that from above, to get the detail in the actual artifact... and to some degree IGNORE the back-lighting from the light-box.
This then is a lighting exercise, and using strong back-light, you will likely just have to 'mess' to get it right.
My first port of call, would be to turn off the light-box & light the subject without it; and just 'expose' for that subject.
When I had an acceptable exposure of that; then I would fix those settings, turn on the light-box and re-shoot, letting the light-box wash-out the back-ground.
THEN, evaluate what I got. Good chance that the light-box will bounce more light onto the subject, off walls or ceiling etc, over-exposing the subject... so I may need to pull the exposure down a tad shortening the shutter speed some.... and see what I get.
But, now the back-ground may be too bright or too grey, so 'some-how' I would need to adjust the lighting balence between suject and back-light, and then tweek the shutter speed to suit, again.
To get more light on the subject, I might use reflectors, even improvised ones like bits of white paper, or scrunched up tin-foil, to bounce more back-light onto it. Or I may move spot-lamps closer to the subject, or use more spot-lights or some mix and match... and more evaluation of results....
The 'angle' of lighting, here will likely be as important as the amount of light, to 'rake' light and get shaddow in texture to reveal detail...
So could take a LOT of messing, to get the most pleasant 'modeling' of the subject... and how brght or dim the back-groud, would become but a minor detail.
BUT, I'd expect lots of trial and error, to get both that flattering subject modeling, more to get the for-ground/back-ground lighting balance, and as much again to tweek exposure to suit with EVERY change I made to subject lighting.
Once I had discovered the 'recipe', t would probably work for pretty much any subject I wanted to drop on the light-box, and might only need a little exposure adjustment one way or another... BUT finding that recipe would NOT be a two second deal, and the camera wont do it all for you.
This IS essentially, a pretty elevated exercise in studio lighting techniques, NOT camera settings or modes. BUT you need to get to grips with both... which is down to practice practice practice.