That turned out to be down to the DHCP options being handed back by our Server 2008 R2 box. Or rather, it was what wasn’t being handed back to the client that was the problem. Linux (and Apple OSX, as it turns out) both want a response to option 119, which defines the domain suffix search order.

Jun 30, 2020 DNS search list on Windows 2008 DHCP server Oct 06, 2011 dhcp-option domain-search not valid??? - OpenVPN Support Forum

Configure DHCP servers - Sophos

Re: LAN domain name and DHCP integration with DNS This is extremely annoying. I used several prior router from different vendors as well as having used dd-wrt and they all seemed to work just fine to add a local lan domain/search domain for local lan dns resolution between lan devices. DHCP: Option domain-search (119) not supported? - CentOS Oct 15, 2009

DHCP provides a framework for passing configuration information to hosts on a TCP/IP network. Configuration parameters and other control information are carried in tagged data items that are stored in the options field of the DHCP message. domain-search 119 Domain Search

Apr 10, 2019 Services — DHCP — Using DHCP Search Domains on Windows Using DHCP Search Domains on Windows DHCP Clients. The DNS Search Domain functionality present in the DHCP Server settings in pfSense® software is only supported by some DHCP clients; pfSense software uses the standard DHCP option 119 mechanism to deliver the search domains to clients which request them. Unfortunately, The Microsoft Windows DHCP client does not support requesting option … finding dns and dhcp servers in a domain - Finding All DHCP Servers In A Domain In order to find the DHCP Servers in your domain, the traditional netsh.exe command line utility will serve you the best if you are using server 2003,2008 or 2008R2 Editions. Again, Open the Command Prompt with elevated Administrative privilege and type the following code: netsh dhcp show server Override DHCP assigned DNS Server and Domain Search in May 17, 2014