Why is the current timecode not visible?

If you've assigned BigTime as a control surface in Final Cut Pro but the current timecode is not displayed on the BigTime window then the likely reason is that the Audio Mixer window is not open.

To open the Audio Mixer:
Choose Tools > Audio Mixer

Final Cut Pro only sends timecode to BigTime if the Audio Mixer is open. The window does not need to be at the front so you can hide it behind other windows and the timecode will still be displayed.