I did some packet-sniffing on my Pockethernet and I've found the cause of the issue.
The tl;dr: With Outgoing VLAN Tag selected, the Pockethernet inserts a request on VLAN1, which some routers and/or switches won't accept and will drop the packet.
Brand-new device, running HW v6 FW v29, App version 2.8a
If you select just Link and DHCP, you get an IP.
If you select just Link, Outgoing VLAN Tag, and DHCP, you don't get an IP.
I captured this with a SonicWALL using the built-in Packet Monitor. This first one is when we were able to get an IP:
Ethernet Header
Ether Type: IP(0x800), Src=[28:fd:80:xx:xx:xx], Dst=[ff:ff:ff:ff:ff:ff]
IP Packet Header
IP Type: UDP(0x11), Src=[0.0.0.0], Dst=[255.255.255.255]
UDP Packet Header
Src=[68], Dst=[67], Checksum=0xcf, Message Length=316 bytes
Application Header
BOOTP:
Value:[0]
Received 0:4294967
Now this time I selected "Outgoing VLAN Tag". Notice the VLAN ID added to the header, and the SonicWALL adding why it was dropped:
Ethernet Header
Ether Type: VLAN ID = 1, Priority = 0
Ether Type: IP(0x800), Src=[28:fd:80:xx:xx:xx], Dst=[ff:ff:ff:ff:ff:ff]
IP Packet Header
IP Type: UDP(0x11), Src=[0.0.0.0], Dst=[255.255.255.255]
UDP Packet Header
Src=[68], Dst=[67], Checksum=0xca9e, Message Length=316 bytes
Application Header
BOOTP:
Value:[0]
DROPPED, Drop Code: 3(Packet on invalid vlan), Module Id: 16(fwCore), (Ref.Id: _1704_kprwvJqqm) 0:0)
I'll post more as I discover things.