tail -f, insert line break after log is idle for 3 seconds?

You could always implement the tail -f (well here, unless you uncomment the seek(), more like tail -n +1 -f as we're dumping the whole file) by hand with perl for instance:

perl -e '
  $| = 1;
  # seek STDIN, 0, 2; # uncomment if you want to skip the text that is
                      # already there. Or if using the ksh93 shell, add
                      # a <((EOF)) after < your-file
  while (1) {
    if ($_ = <STDIN>) {
      print; $t = 0
    } else {
      print "\n"            if $t == 3;
      # and a line of "-"s after 10 seconds:
      print "-" x 72 . "\n" if $t == 10;
      sleep 1;
      $t++;
    }
  }' < your-file

Or let tail -f do the tailing and use perl to insert the newlines if there's no input for 3 seconds:

tail -f file | perl -pe 'BEGIN{$SIG{ALRM} = sub {print "\n"}} alarm 3'

Those assume that the output itself is not slowed down (like when the output goes to a pipe that is not actively read).

bash + date solution:

while IFS= read -r line; do        
    prev=$t         # get previous timestamp value
    t=$(date +%s)   # get current timestamp value
    [[ ! -z "$prev" ]] && [[ "$((t-prev))" -ge 3 ]] && echo ""
    echo "$line"    # print current line
done < <(tail -f error.log)

Python solution (with dynamic time gap argument):

tailing_by_time.py script:

import time, sys

t_gap = int(sys.argv[1])    # time gap argument
ts = 0
while True:
    line = sys.stdin.readline().strip()    # get/read current line from stdin
    curr_ts = time.time()                  # get current timestamp
    if ts and curr_ts - ts >= t_gap:
        print("")                          # print empty line/newline
    ts = curr_ts
    if line:
        print(line)                        # print current line if it's not empty

---

Usage:

tail -f error.log | python tailing_by_time.py 3