Thanks. With a filter of udp.port == 514, it seems there are no messages of that type being received. In the router, I can trigger an "alert" message by going to the shields up website and running a port scan. The router then (usually) shows a "kernel intrusion" alert in its local log but nothing comes up in wireshark.
And you tested your config/test-methodology with other UDP packets ? E.g. if you filter on UDP port 52 (DNS) and then open a bunch of webpages (that you haven't accessed in a while), Wireshark should show you the DNS packets flying around. You probably did that, but just to be sure.
Wireshark doesn't appear in the Windows firewall rules. How does it get round the firewall?
I don't use Windows Firewall (never looked at it). But I expect that you can only set up rules regarding TCP/IP traffic. That means the firewall hooks in the driver stack somewhere after the IP layer.
Wireshark can show all frames on your ethernet wire. Including non-IP stuff. Like ARP or IS-IS. Therefor Wireshark probably hooks into the stack after the Ethernet layer, but before the IP layer. Also, sniffers like Wireshark can set the Ethernet interface in promiscuous mode. Which means the Ethernet interface is going to copy all frames it sees up the stack, even the frames that are not destined for its own MAC address.
So Wireshark will see all frames, even before they reach the MS Firewall.
I've used a command line program called "logger" to generate a syslog message that I type in and that does show up in syslog watcher.
You used that on the same machine as where the syslog daemon is running ? Anyway, your first goal should be to make your router sends out syslog packets.
Set your Wireshark to promiscuous mode. (Mine was set by default).
Make sure the router and your PC are connected directly (no switch in between).
Create events on the router that should send syslog messages.
Watch with Wireshark if any UDP packets get send out, maybe to the wrong IP adress ? There's always a chance that the router tries to send them out over the WAN interface ....
I don't have any other ideas. It's been two decades since I messed around with syslogd myself. Sorry.