http://brushlessgimbal.ca/BRUSHLESS-GIMBAL-PTZ/Gimbal-Brushless-Motor

For what type of tasks you want to use such a gimbal?

Maytech has some very small motors.

It probably would be good to add some mass, and IMU attachment is needed anyway. The cable might be somewhat a problem.

Is there need for the gimbal to be very light, I guess not if you have Raspberry Pi anyway.

http://www.hobbyking.com/hobbyking/store/__9663__HobbyKing_AP_03_7000kv_Brushless_Micro_Motor_3_1g_.html

Start reading upp on winding motors.

copterlab nano-gimbal uses 1806 motors.
they were unwilling to provide brand, or plans for gimbal construction.
SimpleBGC tiny may be knock-off as they advise not to upgrade, as may brick.