Linux/ts

ts

ts adds a timestamp to the beginning of each line of input

The optional format parameter controls how the timestamp is formatted, as used by strftime(3)
The default format is "%b %d %H:%M:%S"

ts 

    # no parameter default  (eg. Aug 03 12:06:32)
-r  # relative time ago (eg. 15m5s ago)
-i  # incremental time since last log  (eg. 00:00:00)
-s  # time since program start  (eg "00:00:00")
-m  # monotonic clock  (eg. Aug 03 12:06:32) 

If you just want the hour/minute/second:

ts "%H:%M:%S"
  12:07:45 xxxxxxxxxxxxxxxxxxx

If you just want epoch timestamp:

ts "%s"
  1722712097 xxxxxxxxxxxxxxxxxxx

Timestamp Output

tail -f /some/device_or_log | ts -s