Reduce 12V battery to 6V for small circuit. You will love it same us.
First choice of Fixed Regulator using family IC-78xx. It is easy to use, cheap, popular for a long time.
I collect these transformerless power supply circuit, use a capacitor instead, it smaller and lighter than transformer. There are circuits as follows.
The simple 6V Power supply circuit. We have a lot of circuits for you. Some ideas may be good for you. All circuits use normal component, easy making.