Verifying that the bug is fixed.

First, reproducing the bug.  After firing up the container, while running "apt install squid dnsmasq -y", I see:

# apt install squid dnsmasq -y
...
Setting up dnsmasq (2.75-1ubuntu0.16.04.5) ...
Job for dnsmasq.service failed because a timeout was exceeded. See "systemctl status dnsmasq.service" and "journalctl -xe" for details.
invoke-rc.d: initscript dnsmasq, action "start" failed.
● dnsmasq.service - dnsmasq - A lightweight DHCP and caching DNS server
   Loaded: loaded (/lib/systemd/system/dnsmasq.service; enabled; vendor preset: enabled)
  Drop-In: /run/systemd/generator/dnsmasq.service.d
           └─50-dnsmasq-$named.conf, 50-insserv.conf-$named.conf
   Active: failed (Result: timeout) since Wed 2020-09-16 15:43:01 UTC; 11ms ago
  Process: 1565 ExecStartPost=/etc/init.d/dnsmasq systemd-start-resolvconf (code=killed, signal=TERM)
  Process: 1554 ExecStart=/etc/init.d/dnsmasq systemd-exec (code=exited, status=0/SUCCESS)
  Process: 1553 ExecStartPre=/usr/sbin/dnsmasq --test (code=exited, status=0/SUCCESS)
 Main PID: 1564 (code=exited, status=0/SUCCESS)

Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: started, version 2.75 cachesize 150
Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: compile time options: IPv6 GNU-getopt DBus i18n IDN DHCP DHCPv6 no-Lua TFTP conntrack ipset auth DNSSEC loop-detect inotify
Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: DNS service limited to local subnets
Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: read /etc/hosts - 7 addresses
Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: reading /var/run/dnsmasq/resolv.conf
Sep 16 15:41:31 squid-bug1761096 dnsmasq[1564]: using nameserver 10.101.133.1#53
Sep 16 15:43:01 squid-bug1761096 systemd[1]: dnsmasq.service: Start-post operation timed out. Stopping.
Sep 16 15:43:01 squid-bug1761096 systemd[1]: Failed to start dnsmasq - A lightweight DHCP and caching DNS server.
Sep 16 15:43:01 squid-bug1761096 systemd[1]: dnsmasq.service: Unit entered failed state.
Sep 16 15:43:01 squid-bug1761096 systemd[1]: dnsmasq.service: Failed with result 'timeout'.
...

We also see the bug happening while restarting the dnsmasq.service:

# systemctl restart dnsmasq.service 
Job for dnsmasq.service failed because a timeout was exceeded. See "systemctl status dnsmasq.service" and "journalctl -xe" for details.
# systemctl status dnsmasq.service 
● dnsmasq.service - dnsmasq - A lightweight DHCP and caching DNS server
   Loaded: loaded (/lib/systemd/system/dnsmasq.service; enabled; vendor preset: enabled)
  Drop-In: /run/systemd/generator/dnsmasq.service.d
           └─50-dnsmasq-$named.conf, 50-insserv.conf-$named.conf
   Active: failed (Result: timeout) since Wed 2020-09-16 15:47:22 UTC; 17s ago
  Process: 1744 ExecStop=/etc/init.d/dnsmasq systemd-stop-resolvconf (code=killed, signal=TERM)
  Process: 1808 ExecStartPost=/etc/init.d/dnsmasq systemd-start-resolvconf (code=killed, signal=TERM)
  Process: 1799 ExecStart=/etc/init.d/dnsmasq systemd-exec (code=exited, status=0/SUCCESS)
  Process: 1798 ExecStartPre=/usr/sbin/dnsmasq --test (code=exited, status=0/SUCCESS)
 Main PID: 1807 (code=exited, status=0/SUCCESS)

Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: compile time options: IPv6 GNU-getopt DBus i18n IDN DHCP DHCPv6 no-Lua TFTP conntrack ipset auth DNSSEC loop-detect inotify
Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: DNS service limited to local subnets
Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: no servers found in /var/run/dnsmasq/resolv.conf, will retry
Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: read /etc/hosts - 7 addresses
Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: reading /var/run/dnsmasq/resolv.conf
Sep 16 15:45:52 squid-bug1761096 dnsmasq[1807]: using nameserver 10.101.133.1#53
Sep 16 15:47:22 squid-bug1761096 systemd[1]: dnsmasq.service: Start-post operation timed out. Stopping.
Sep 16 15:47:22 squid-bug1761096 systemd[1]: Failed to start dnsmasq - A lightweight DHCP and caching DNS server.
Sep 16 15:47:22 squid-bug1761096 systemd[1]: dnsmasq.service: Unit entered failed state.
Sep 16 15:47:22 squid-bug1761096 systemd[1]: dnsmasq.service: Failed with result 'timeout'.

Now, installing the package containing the proposed fix, and testing that it works.  After installing, restarting dnsmasq.service multiple times and verify that it always succeeds:

# systemctl restart dnsmasq.service && echo $?
0
# systemctl restart dnsmasq.service && echo $?
0
# systemctl restart dnsmasq.service && echo $?
0
# systemctl restart dnsmasq.service && echo $?
0
# systemctl restart dnsmasq.service && echo $?
0

Therefore, tagging the bug as verified for Xenial.