If you want a brighter bulb, I recommend staying away from LEDs for the backup lights. I bought a white 24-LED bulb for my '02 and it put out less light than the stock incandescent. (and it wasn't cheap) You may be able to use a slightly higher wattage stock-type bulb and see what that does for you. Unlike an incandescent bulb, the light from LED's is focused in one direction. The stock tail lamp lense on my '02 Silvy is designed to focus the scattered light from an incandescent so it probably isn't optimized for the focused and narrow beam of a LED.

I know you don't want to but if you're serious about more light out back, you may have to go with auxiliary back-up lighting.

Good luck.