First - and this is a minor point - 'Jacuzzi' is a brand name, and it makes people think you are asking about that brand of tub. You have a Diamonte - with Balboa goodies. I know, I know - picky picky!
Is this light the type which plugs into a 12v socket? Many tubs came with a 12v light bulb, but there are companies who sell cool little units which simply plug into the socket and have LED technology. Some change colors, etc.
If so, you could get a 12v bulb and plug it into the socket and see if the trouble is in the LED unit or the power being supplied TO that socket. Here's one of those LED kits:
Here's the socket and bulb before adding the above in place of the bulb. Actually, this is the whole enchilada: bulb and socket are near the bottom center, lens is upper left, snap-on colored lenses upper right.