The gimbal configuration message set uses a number of commands and few special-purpose messages to configure a payload mount.
By default the gimbal should be communicating with the component ID MAV_COMP_ID_GIMBAL.
The two main commands to use mavlink gimbals are MAV_CMD_DO_MOUNT_CONFIGURE and MAV_CMD_DO_MOUNT_CONTROL.
Another possible control command would be MAV_CMD_DO_MOUNT_CONTROL_QUAT. This command does not seem to be implemented by any systems at time of writing.
To reboot or shut down a gimbal send the command MAV_CMD_PREFLIGHT_REBOOT_SHUTDOWN. The options to be set for the gimbal are found in param4.
Note This is the same message/process as for autopilot systems.
A gimbal (or mount) should send a HEARTBEAT (e.g. every second) just like any other MAVLink component. Additionally, it can send feedback about the angles it's pointing using the message MOUNT_ORIENTATION.