In OpenVR, base stations are "tracked devices", just like the controllers and HMD. The standard SteamVR plugin for Unity already has a way to get the position of any tracked device, see for example how the controllers are implemented in the standard [CameraRig]
prefab.
The only problem is that you need to provide the "index" of the device, which may change every time you reconnect your headset. SteamVR plugin handles this with the SteamVR_ControllerManager
component, but as the name suggests - it handles only controllers. You should be able to implement something similar, or just edit the script and find the lines
if (deviceClass == ETrackedDeviceClass.Controller ||
deviceClass == ETrackedDeviceClass.GenericTracker)
and add ETrackedDeviceClass.TrackingReference
to this list. You should then be able to copy the controller objects and attach them in the "additional objects" array in SteamVR_ControllerManager
to have the base stations appear in your scene.