Currently, the motion webcam server, as activated by the webcam_port
configuration directive, only listens on IPv4, as seen in this output
from ss -lnp:

Recv-Q Send-Q  Local Address:Port  Peer Address:Port
0      10      *:8081              *:*              users:(("motion",13749,6))

The local address:port should look like this: :::8081.

There has been some work on this upstream, including patches:
http://www.lavrsen.dk/foswiki/bin/view/Motion/FeatureRequest2011x01x06x052631

Dear Maintainer,

There is a dual problem to this bug: the configuration interface *only*
listens on IPv6. I think this is the same problem. I've seen this on two
different machines.

   * What led up to the situation?

Set the following in the configuration file:

  ipv6_enabled on
  stream_port 8281
  stream_localhost off
  webcontrol_port 8280
  webcontrol_localhost off

   * What was the outcome of this action?

- Configuration server listen on IPv6 only,
- Streaming server listens on IPv4 only

netstat -ln shows the following

  tcp        0      0 0.0.0.0:8281            0.0.0.0:* LISTEN
  tcp6       0      0 ::1:8280                :::* LISTEN

   * What outcome did you expect instead?

Both configuration and streaming server listen on both IPv4 and IPv6,
i.e.,

  tcp        0      0 0.0.0.0:8280            0.0.0.0:* LISTEN
  tcp        0      0 0.0.0.0:8281            0.0.0.0:* LISTEN
  tcp6       0      0 ::1:8280                :::* LISTEN
  tcp6       0      0 ::1:8281                :::* LISTEN