reset-elapsed() {
  (( last_cmd_at = SECONDS ))
}

ping-timer() {
  kill -USR1 "$reaper_pid" 2>/dev/null
}

kill-reaper() {
  kill -KILL "$reaper_pid"
}

{
  trap reset-elapsed USR1
  last_cmd_at=0

  while sleep 1; do
    (( elapsed = SECONDS - last_cmd_at ))

    if (( elapsed > 600 )); then
      kill -KILL "$$"
      exit
    fi
  done
} &

reaper_pid=$! prompt_cmds+=(ping-timer)
trap kill-reaper EXIT