Ticking Never forward non-FQDN queries would do the opposite of what you want to achieve: It would prevent any request for a non-dot domain to be forwarded. That setting needs to be unticked.
For such non-dot requests for local hostnames to be resolved successfully, you'd need matching DNS entries to be defined somewhere, either by Pi-hole or by some other DNS server in your network.
If another DNS server holds those records, you'd have to configure Pi-hole's Conditional Forwarding to that DNS server.
Your debug log indicates you've correctly configured Conditional Forwarding to your router at 10.11.12.1:
revServers = [
"true,10.11.12.0/24,10.11.12.1#53,your.domain"
] ### CHANGED, default = []
However, you've also added a custom dnsmasq configuration, which would conflict with Pi-hole's Conditional Forwarding:
-rw-r--r-- 1 root root 63 Mar 2 20:55 /etc/dnsmasq.d/99-your.domain.conf
server=/your.domain/#
address=(…)
That first line configures Pi-hole to use its standard servers for your.domain, i.e. its configured upstreams.
You should remove that custom configuration.
In addition, you want to verify that your router is correctly answering local DNS requests, e.g. by requesting resolution for a local hostname directly from your router:
nslookup <hostname> 10.11.12.1
If that does return NXDOMAIN, it would demonstrate that your router doesn't keep DNS records for local hostnames, so configuring Conditional Forwarding would be futile.
Instead, you'd have to create Local DNS Records in Pi-hole.
And some remarks on your router's/network's IPv6 DNS configuration (click for details)
Your debug log indicates that your router advertises its own IPv6 GUA as DNS server. This would have IPv6 clients to by-pass Pi-hole via your router.
You'd have to find a way to configure your router to stop advertising its own IPv6 as DNS server, or to advertise your Pi-hole host machine's IPv6.
You'd have to consult your router's documentation sources on further details for its IPv6 configuration options.
If your router doesn't support configuring IPv6 DNS, you could consider disabling IPv6 altogether, provided you'd not depend on IPv6 for reasons.
If your router doesn't support that either, your IPv6-capable clients will always be able to bypass Pi-hole via IPv6.
You could then try to mitigate this, by setting Pi-hole as the only upstream of your router, provided your router supports it.
But note that you won't be able to attribute DNS requests to original individual IPv6 clients in such a configuration.
In addition, there is another router advertising a different local search domain:
*** [ DIAGNOSING ]: Discovering active DHCP servers (takes 6 seconds)
Scanning all your interfaces for DHCP servers and IPv6 routers
Timeout: 6 seconds
* Received 56 bytes from fe80::<redacted> @ eth0
Hop limit: 64
Stateful address conf.: Yes
Stateful other conf.: Yes
(…)
DNS search list: <redacted>.org
DNS search list lifetime: 1800 sec
MTU: 1500 bytes (valid)
If that's by intention, you may want to consider also configuring Conditional Forwarding for that domain.