First, check out my Mouse Taxidermy
Instructable. It covers all of the basic skills and tools you'll need to prepare your rat for its LED Throwiedom. Mice are smaller and easier to work with than rats, so I'd definitely recommend trying this with a mouse first.
There's no reason you can't make a Mouse LED Throwie; I just happened to have both a frozen rat and red LEDs of the proper size for rat eyes. I'll make some mouse LED throwies next, but it's really all the same thing. I'll put up pictures when I make the mice.
The rodents below are quick-thawing in lukewarm water; this is suboptimal and can be avoided through proper planning.
If you're ethically opposed to the concept of creative and/or decorative taxidermy (and have chosen to look anyway) I have two questions for you: do you wear leather, and do you eat meat? If you answered yes to either, can you/would you kill and prepare the animals necessary to procure this meat and leather? Willfully ignoring the source of your food and clothing hypocritically outsources the ethical questions and is ultimately disrespectful to the animals involved. If you're an ethical vegan and eschew leather, I respect your opinion and your desire to avoid viewing discomfiting images. Thus I carefully label the Intro page of these Instructables, hide the more graphic pictures on the later pages, and promise not to send you any taxidermy for Christmas.
Now back to your regularly scheduled Instructable.