So last week I started to look for the circuit's missing C2 race since asking around and checking now and then yielded nothing. On the plus side, I have found a pattern for the races but no variation that suggests a "preparation" for a C2 race or something. DAT mining also suggests that C1 is an event-only race, but also that C2 is a regular race somehow. In any case, here's the daily pattern, although it's nothing complicated.
Code:
Signup times for Chocobo Races
Time in japan standard

0:00 C4     4:00 C4     8:00 C4   12:00 C4   16:00 C4   20:00 C4
0:15 C4     4:15 C4     8:15 C4   12:15 C4   16:15 C4   20:15 C4
0:30 C4     4:30 C4     8:30 C4   12:30 C4   16:30 C4   20:30 C4
0:45 C3     4:45 C3     8:45 C3   12:45 C3   16:45 C3   20:45 C3
1:00 C4     5:00 C4     9:00 C4   13:00 C4   17:00 C4   21:00 C4
1:15 C4     5:15 C4     9:15 C4   13:15 C4   17:15 C4   21:15 C4
1:30 C4     5:30 C4     9:30 C4   13:30 C4   17:30 C4   21:30 C4
1:45 C3     5:45 C3     9:45 C3   13:45 C3   17:45 C3   21:45 C3
2:00 C4     6:00 C4    10:00 C4   14:00 C4   18:00 C4   22:00 C4
2:15 C4     6:15 C4    10:15 C4   14:15 C4   18:15 C4   22:15 C4
2:30 C4     6:30 C4    10:30 C4   14:30 C4   18:30 C4   22:30 C4
2:45 C3     6:45 C3    10:45 C3   14:45 C3   18:45 C3   22:45 C3
3:00 C4     7:00 C4    11:00 C4   15:00 C4   19:00 C4   23:00 C4
3:15 C4     7:15 C4    11:15 C4   15:15 C4   19:15 C4   23:15 C4
3:30 C3     7:30 C3    11:30 C3   15:30 C3   19:30 C3   23:30 C3
3:45 C3     7:45 C3    11:45 C3   15:45 C3   19:45 C3   23:45 C3
So any clues as to when C2 might happen? If it's even in the bloody game...