After I've fixed the default routing in my home office, I've stumbled across another problem: the two ISPs I'm using for my primary and backup link have DNS servers that reply solely to the DNS requests sent from their own IP address range:

When the traffic is switched from the primary to the backup ISP, I therefore also need to switch the DNS servers. Fortunately, this is quite easy to do on a router; you just need to configure ppp ipcp dns request on the dialer interface and the router starts asking for the DNS server address as part of the IPCP negotiation.

The negotiation process can be debugged with the debug ppp negotiation command; it's a bit more complex than usual in my case since the access server has no secondary DNS (only the primary DNS is configured):

Se1/0 IPCP: O CONFREQ [Closed] id 1 len 22
Se1/0 IPCP:    Address 0.0.0.0 (0x030600000000)
Se1/0 IPCP:    PrimaryDNS 0.0.0.0 (0x810600000000)
Se1/0 IPCP:    SecondaryDNS 0.0.0.0 (0x830600000000)
Se1/0 PPP: Process pending ncp packets
Se1/0 IPCP: Redirect packet to Se1/0
Se1/0 IPCP: I CONFREQ [REQsent] id 1 len 10
Se1/0 IPCP:    Address 10.0.0.33 (0x03060A000021)
Se1/0 IPCP: O CONFACK [REQsent] id 1 len 10
Se1/0 IPCP:    Address 10.0.0.33 (0x03060A000021)
Se1/0 IPCP: I CONFREJ [ACKsent] id 1 len 10
Se1/0 IPCP:    SecondaryDNS 0.0.0.0 (0x830600000000)
Se1/0 IPCP: O CONFREQ [ACKsent] id 2 len 16
Se1/0 IPCP:    Address 0.0.0.0 (0x030600000000)
Se1/0 IPCP:    PrimaryDNS 0.0.0.0 (0x810600000000)
Se1/0 IPCP: I CONFNAK [ACKsent] id 2 len 16
Se1/0 IPCP:    Address 10.0.0.34 (0x03060A000022)
Se1/0 IPCP:    PrimaryDNS 10.0.0.10 (0x81060A00000A)
Se1/0 IPCP: O CONFREQ [ACKsent] id 3 len 16
Se1/0 IPCP:    Address 10.0.0.34 (0x03060A000022)
Se1/0 IPCP:    PrimaryDNS 10.0.0.10 (0x81060A00000A)
Se1/0 IPCP: I CONFACK [ACKsent] id 3 len 16
Se1/0 IPCP:    Address 10.0.0.34 (0x03060A000022)
Se1/0 IPCP:    PrimaryDNS 10.0.0.10 (0x81060A00000A)
Se1/0 IPCP: State is Open

The results can be inspected only with the show host command:

GW#show host
Default domain is not set
Name/address lookup uses domain service
Name servers are 10.0.0.10

The access server receiving the call requires no special configuration; the first IP address configured with the ip name-server command is used as the primary DNS and the second one as the secondary. Alternatively, you can configure a different set of DNS servers to pass to the client with the ppp ipcp dns primary-DNS-address secondary-DNS-address interface configuration command.

Unfortunately, the integration with LAN clients is not as seamless as with DHCP; to make the whole solution work, you have to configure the router as a forwarding DNS server and make the LAN clients use the router as the default gateway and DNS server with the DHCP pool configuration:

ip dns server
!
ip dhcp pool LAN
   import all
   network 192.168.0.0 255.255.255.240
   default-router 192.168.0.1
   dns-server 192.168.0.1