Reisen is a soldier, a veteran from the first Lunar Civil War roughly a thousand years ago. She was on the side of the rebels. Naturally, the rebels lost. As a survivor and a respected enemy commander, Reisen was made into a pet by the victorious Watatsuki sisters and lived that way for a significant portion of her life. It wasn't a bad life, but she disliked it all the same.
When Neil Armstrong landed on the moon, oblivious to the Lunarian society, and the Lunarians promptly assumed it was an armed invasion, Reisen threw up her hands. With Toyohime pressing her to train the new lunar rabbit corps, she instead went AWOL. Her last words before leaving the moon, reportedly, were "This is stupid. I'm leaving."
She appeared on Earth in 1969 Japan, seeking out the infamous princess Houraisan and Dr. Yagokoro who'd disappeared on Earth ages ago. When Reisen found her way into Gensokyo (as youkai tend to do), she found the people she was looking for. Reisen wasted little time casting her lot in with her fellow Lunarians-in-exile, acting as a bodyguard for Kaguya and ... attempting... to mentor Tewi into a more responsible rabbit.
Following the Stolen Moon incident, she's been learning the art of doctoring from Eirin and has taken to selling medicines in the village once a week.
Reisen is very atypical for a youkai, as one who associates easily with humans. However, pinning down her personality type is quite difficult as she is fundamentally not of this world and therefore does not adhere to the same set of rules. In fact, Reisen can completely change her personality at will in response to any given situation. Typically, she prefers a level-headed approach. She takes things seriously, and tends to look for peaceful resolutions to conflicts wherever possible. At the same time, though, Reisen is quite obedient as a bodyguard, and can be a terrifying combatent due to the perception-warping nature of her powers. In spite of her loyalty and strength, around Eientei, she's something of a doormat and usually winds up being the only person in the great mansion who actually does any real work.
'Wavelengths' includes obvious things like light and sound (to become invisible and unhearable). However, Reisen is best known for inducing madness. This is because she can even mess with brainwaves. A shorter wavelength results in madness, while a longer wavelength causes carefree behavior.