Yes—reduce the lightbox lighting so the bear’s internal glow is closer in brightness to the scene lighting. Then use a longer exposure to gather more of the LED’s light while still showing the bear.

If you’re using strobes/speedlights, turn their power way down. A longer shutter speed won’t affect the brief flash much, but it will record more of the constantly glowing LED. You may also need to raise ISO.

If you’re using continuous lights, use much dimmer lamps and expose longer.

If the difference is still too great, a single photo may not show both convincingly. In that case, the most honest and visually effective option is often to show two images side by side: one bright “product” shot and one darker shot that emphasizes the glow. A composite of two exposures is possible, but it won’t be a fully accurate single photograph.