output on a rotating stator with that coil arrangement is always gonna be AC. it should get up to 14v or higher as rpm goes up, 3v at idle is low but not surprising really.
The easiest way to wire a brakelight from that is direct with a "normally-closed" brakelight switch. depending on your bike your brakelight switches may already be normally closed. What normally closed means is it's a closed circuit when the button is NOT pressed. it's kinda confusing because the brake lever is normally pressing it. so when you pull the brake lever it releases the switch button and it returns to it's "normal" closed position, closing the circuit. so you have power going into one side of the brake switch and out the other side to the brakelight, when you pull lever, switch closes the circuit, lights up the brakelight. win.
The "hookup" page section here has some useful doodles and explanation for how to hook it up with a normally closed or normally open type switches. Just a little abstract thinking to make the wiring fit to your setups. https://www.mopedarmy.com/wiki/DIY_Brake_Light