The pulse glow might take time, but you could probably find some other product that pulses an LED in the way you want, and use that to pulse your own lights.
If I understand right, you have a solid opaque ball, but a translucent case around it? If that's what you have, I think the easiest way to get it glowing would be to buy cold cathode lights. You can find them at most online computer case shops, especially those that sell really cool looking cases and/or cater to "case mod" types. They're nice and bright, don't heat up much, and are designed to run off the power supply in a PC.
If not that, you can get super-bright LEDs from a variety of places, including
http://www.theledlight.com/, though it would be harder to wire up than cold cathode lights, and would give more of a spotlight effect than a smooth glow.
Or just chuck a 40-watt light bulb underneath the thing in your panel...