RCON is not listening on port

When vanilla 1.13.1 server starts, it reports RCON is listening:
[13:41:43] [RCON Listener #1/INFO|#1/INFO]: RCON running on 0.0.0.0:61632

However, there is actually nothing listening on that port:
$ lsof -n | grep LISTEN
java 62221 minecraft 30u IPv6 0t0 TCP *:61631 (LISTEN)

Any attempt to connect naturally fails with "Connection refused"
There are no errors whatsoever reported by the server; as far as it is concerned, everything is OK. If you stop/restart the server several times - on average (for me), 12 times - you may get lucky and RCON will actually start listening. Rebooting the host does not influence chance of success.

Apparently this is not a new issue; see MC-81879