How to check status of the console cable connection?

Are you asking how can you tell if someone is logged in to the console? I would run something like last and see if there are any ttyS0 logins (like the first line, especially if the last part says "still logged in").

[root@bigip1:online:In Sync] config  last
root    ttyS0                       Sat Nov 15 12:47 - 21:48 (31+12:37)
root    pts/1   55.98.0.130         Fri Nov 14 18:52 - 22:16 (03:23)
root    pts/0   c-57-161-249-108    Fri Nov 14 05:45 - 03:09 (1+21:23)
root    pts/1   c-57-161-249-108    Tue Nov 11 19:53 - 05:03 (09:09)
root    pts/1   55.98.0.130         Wed Nov 5 07:35 - 11:14 (03:39)
root    pts/0   c-57-161-249-108    Wed Nov 5 06:20 - 21:10 (6+14:49)
root    pts/0   55.98.0.130         Tue Nov 4 13:32 - 14:02 (00:30)