I live in Kaiserslautern Germany and Ramstein is about 10km west. I haven't exploited any siblings, but am a little familiar with the rules/regulations locally for US military licensing/registration with USAREUR. Is your brother with the military?
Probably cheaper to buy locally, but then you have the registration issue to address if you don't have a bike you want to ship. You might be able to buy here and register in the states depending on the state. You will not be able to register the bike in your name here. Your brother will be able to register bikes with the military (USAREUR), but then there are restrictions on operation of the bikes (need specific approval for non-USAREUR licensed person) and a limitation on how many can be registered. Each family gets three personally owned vehicles and two recreational vehicles. More are allowed with a waiver approved by the individual's commander. It would be possible for your brother to register the bike and you ride if you go through the process to get approval. A little bit of a pain, but doable.
If you ship your bike and leave US plates on it or buy in Germany and register in the states, you could leave it here and get insurance when needed if it will be stored off base. You would need international insurance, or "green card" insurance (the insurance paper is green). Stefan Knopf arranges shipping, rents bikes, stores bikes, arranges green card insurance for the needed time period, etc. His site is http://www.knopftours.com/Web-Site/Welcome.html
. He stores hundreds of bikes, most of which are from the states and keep US registration. He is in Heidelberg, a little over an hour away. Don't know if he would get you green card insurance if not stored with him.
If you want, send me a PM with email address and I'll send you information on the requirements for you to get approval, regulation governing licensing, etc.