There's really nothing to worry about - what you're seeing are ICMP redirects, and they are not a problem as such.
The reasoning behind what you're seeing is this:
Your MBP usually has the MAC address of wwwelc in its ARP cache. Similarly, SWITCH1 and SWITCH2 knows on which of their ports the computer with the MAC-address of wwwelc is connected. This means that it can send IP packets directly to the MAC address of wwwelc.
When you power off the Mac Mini and some time passes, the MAC address will eventually be flushed from the caches on your switches and/or the ARP cache on the MBP.
Imagine that it is no longer in the cache on the switch. This means that the switch has no choice than to broadcast packets for that MAC-address to all its ports. This means the SWITCH1 will send the packet to both the Time Capsule as well as SWITCH2.
The Time Capsule receives the packet and acts as a router. It will try to route the packet to its destination. It finds that the packet is actually destined for something on the ethernet connection on which it came into the Time Capsule - i.e. it is not to be routed out with the WiFi or Internet connection ports.
For that situation, we have something called ICMP redirects. It is common to many routers from various producers - so it's not Time Capsule specific.
The Time Capsule sends out the ICMP redirect to be "nice". It is letting the sender know that it received a packet where the sender could actually have sent it directly to the next hop of the route without involving the Time Capsule. So it is letting it know that it could have saved a hop.
I.e. the following conditions are met:
The packet came in on the same port that it is going to be routed out of
The network (subnet) of the source IP is the same network as the next hop (i.e. the sender could just have sent it directly to that next-hop)
The packet is not source routed (i.e. the sender did not instruct a specific path to be taken)
So that's the explanation for what you're seeing. The Time Capsule receives the packet because the SWITCH or MBP doesn't know where to send the packet - so it broadcasts it. The Time Capsule is trying to be nice, saying that the packet could have been delivered in an easier way. And finally, the destination wwwelc is still down, so you're not going to get any replies from the destination of course.
Best Answer
The obvious thing to check is if you have FileVault enabled and attach a display simulator dongle. In the FileVault case, the machine does not restart to the OS but to a firmware / limited log in screen, but having a display connected won’t enable/disable FileVault.
You will want to have a remote KVM or someone that can log in for unexpected power failures. See this thread for a lot more options like power, display and management options for headless Macs.