Wait for service to gracefully exit before machine shutdown/reboot

How do you write a systemd service that gracefully shuts down upon machine shutdown or reboot? In particular, it should delay machine shutdown until it exits gracefully.

I have a service that takes 10 seconds to shut down: /usr/local/bin/shutdowntest.sh:

#!/bin/bash

SHUTDOWN=0
SHUTDOWN_TIME=10
TRAPPED_SIGNAL=

function onexit() {
  TRAPPED_SIGNAL=$1
  SHUTDOWN=1
}

for SIGNAL in SIGINT SIGTERM SIGHUP SIGPIPE SIGALRM SIGUSR1 SIGUSR2; do
  trap "onexit $SIGNAL" $SIGNAL
done

echo >&2 "shutdowntest running"
while ((!SHUTDOWN || SHUTDOWN_TIME>0)); do
  if [[ -n "$TRAPPED_SIGNAL" ]]; then
    echo >&2 "shutdowntest received signal $TRAPPED_SIGNAL"
    TRAPPED_SIGNAL=
  elif ((SHUTDOWN)); then
    echo >&2 "shutdowntest Shutting down: $SHUTDOWN_TIME more sleeps"
    SHUTDOWN_TIME=$((SHUTDOWN_TIME-1))
    sleep 1
  else
    sleep 10
  fi
done
echo >&2 "shutdowntest Finished shutting down; quitting"

I set TimeoutStopSec to 15s in /etc/systemd/system/shutdowntest.service:

[Service]
ExecStart=/usr/local/bin/shutdowntest.sh
TimeoutStopSec=15

[Install]
WantedBy=multi-user.target

When I run sudo systemctl stop shutdowntest.service, the service shuts down gracefully according to /var/log/syslog:

00:57:11 shutdowntest.sh[1980]: shutdowntest received signal SIGTERM
00:57:11 shutdowntest.sh[1980]: shutdowntest Shutting down: 10 more sleeps
00:57:11 systemd[1]: Stopping shutdowntest.service...
00:57:11 shutdowntest.sh[1980]: Terminated
00:57:11 shutdowntest.sh[1980]: shutdowntest Shutting down: 9 more sleeps
00:57:12 shutdowntest.sh[1980]: shutdowntest Shutting down: 8 more sleeps
00:57:13 shutdowntest.sh[1980]: shutdowntest Shutting down: 7 more sleeps
00:57:14 shutdowntest.sh[1980]: shutdowntest Shutting down: 6 more sleeps
00:57:15 shutdowntest.sh[1980]: shutdowntest Shutting down: 5 more sleeps
00:57:16 shutdowntest.sh[1980]: shutdowntest Shutting down: 4 more sleeps
00:57:17 shutdowntest.sh[1980]: shutdowntest Shutting down: 3 more sleeps
00:57:18 shutdowntest.sh[1980]: shutdowntest Shutting down: 2 more sleeps
00:57:19 shutdowntest.sh[1980]: shutdowntest Shutting down: 1 more sleeps
00:57:20 shutdowntest.sh[1980]: shutdowntest Finished shutting down; quitting
00:57:20 systemd[1]: Stopped shutdowntest.service.

But when I sudo reboot or sudo shutdown now the machine, the service is killed without enough time to exit gracefully, and the /var/log/syslog ends only 1s later.

00:59:30 shutdowntest.sh[2014]: Terminated
00:59:30 shutdowntest.sh[2014]: shutdowntest received signal SIGTERM
00:59:30 shutdowntest.sh[2014]: shutdowntest Shutting down: 10 more sleeps
00:59:30 systemd[1]: Stopping shutdowntest.service...

How to ensure that the service is given the time (TimeoutSec or TimeoutStopSec) to exit when the machine is shutdown or rebooted?