Several questions on your questions...
"A more natural look"
First of all. Photography is not just about light, it is also about shadows.
On a reflective object, it is not just about reflections of light sources, but also of dark surroundings.
As we do not live in a "heaven-like place" with light, and just light all around us, a lightbox looks not that natural.
So, my first answer is, add some "negative lights". These are black cardboard or paper in some places.
Try adding one full wall or two and see where this black is now shown on your watch.
"The photo is too dark"
Do not use auto exposure. Use manual mode.
Having the right exposure to a completely white place is about knowing the dynamic range on your camera. You have to know your histogram. Let me explain.
If you have access to a gray card (you could DIY*) you should have on your histogram a strong line at the center of it.
Using the same exact exposition now take a picture of a white sheet of paper. Stack two or 3 of them so you have a "whiter" target.
Now, look at your histogram. That is where that white on that light condition should look like.
The histogram of a reflective surface is different, because you can actually blow the whites on a reflection, and that is totally ok.
Do the same with a really black cloth, like black velvet. Now you will have a spike on the black on that light situation.
Now you have something to compare the histogram of the background of your light tent using that exposure.
Of course, you can just add one or two stops to your shutter speed.
- A DIY gray card can be done by printing a checkboard pattern. Try let's say squares of 2-3mm
Of course, it will depend on the quality of the printer. Try using laser-based print with a really good deep black toner using extra white paper.
In time use this technique to find the right exposure using white paper or a white wall and then compensating the f-stops so your photos are not dark.
If you want to fix the dark look in post, you can blow some whites on your histogram. Just keep the white on the background natural.
Te reflection of yourself on the watch cover
Take a look: How to shoot a reflection in a ball bearing without appearing in it?
In your case, remove the white wall on the side where the camera is. Now turn off all lights outside. Move the camera further away and now you will reduce that reflection because it would be less stuff to reflect on in the first place.
Watch your framing. The first image needs more room on the top.