I found a better log file to watch, /etc/daemon.log:
May 27 19:40:59 myhost pppd[3734]: pppd 2.4.4 started by , uid 1001
May 27 19:40:59 myhost pppd[3734]: using channel 3
May 27 19:40:59 myhost pppd[3734]: Using interface ppp0
May 27 19:40:59 myhost pppd[3734]: Connect: ppp0 <--> /dev/tts/1
May 27 19:40:59 myhost pppd[3734]: sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth pap> <magic 0x5be9ebea> <pcomp> <accomp>]
May 27 19:40:59 myhost pppd[3734]: rcvd [LCP ConfReq id=0x2a <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:40:59 myhost pppd[3734]: sent [LCP ConfAck id=0x2a <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:40:59 myhost pppd[3734]: rcvd [LCP ConfReq id=0x2b <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:40:59 myhost pppd[3734]: sent [LCP ConfAck id=0x2b <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:41:00 myhost pppd[3734]: rcvd [LCP ConfReq id=0x2c <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:41:00 myhost pppd[3734]: sent [LCP ConfAck id=0x2c <asyncmap 0x0> <pcomp> <accomp> <magic 0x6ced>]
May 27 19:41:02 myhost pppd[3734]: sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth pap> <magic 0x5be9ebea> <pcomp> <accomp>]
May 27 19:41:02 myhost pppd[3734]: rcvd [LCP ConfAck id=0x1 <asyncmap 0x0> <auth pap> <magic 0x5be9ebea> <pcomp> <accomp>]
May 27 19:41:02 myhost pppd[3734]: rcvd [PAP AuthReq id=0x4 user="pppuser" password=<hidden>]
May 27 19:41:02 myhost pppd[3734]: user pppuser logged in
May 27 19:41:02 myhost pppd[3734]: sent [PAP AuthAck id=0x4 "Login ok"]
May 27 19:41:02 myhost pppd[3734]: PAP peer authentication succeeded for pppuser
May 27 19:41:02 myhost pppd[3734]: sent [CCP ConfReq id=0x1 <deflate 15> <deflate(old#) 15> <bsd v1 15>]
May 27 19:41:02 myhost pppd[3734]: sent [IPCP ConfReq id=0x1 <compress VJ 0f 01> <addr 192.168.2.1>]
May 27 19:41:02 myhost pppd[3734]: rcvd [IPCP ConfReq id=0x7 <addr 0.0.0.0> <ms-dns1 0.0.0.0> <ms-dns3 0.0.0.0> <compress VJ 0f 00>]
May 27 19:41:02 myhost pppd[3734]: sent [IPCP ConfNak id=0x7 <addr 192.168.2.2> <ms-dns1 68.94.156.1> <ms-dns3 68.94.157.1>]
May 27 19:41:02 myhost pppd[3734]: rcvd [LCP ProtRej id=0x4 80 fd 01 01 00 0f 1a 04 78 00 18 04 78 00 15 03 2f]
May 27 19:41:02 myhost pppd[3734]: Protocol-Reject for 'Compression Control Protocol' (0x80fd) received
May 27 19:41:02 myhost pppd[3734]: rcvd [IPCP ConfAck id=0x1 <compress VJ 0f 01> <addr 192.168.2.1>]
May 27 19:41:03 myhost pppd[3734]: rcvd [IPCP ConfReq id=0x8 <addr 192.168.2.2> <ms-dns1 68.94.156.1> <ms-dns3 68.94.157.1> <compress VJ 0f 00>]
May 27 19:41:03 myhost pppd[3734]: sent [IPCP ConfAck id=0x8 <addr 192.168.2.2> <ms-dns1 68.94.156.1> <ms-dns3 68.94.157.1> <compress VJ 0f 00>]
May 27 19:41:03 myhost pppd[3734]: Cannot determine ethernet address for proxy ARP
May 27 19:41:03 myhost pppd[3734]: local IP address 192.168.2.1
May 27 19:41:03 myhost pppd[3734]: remote IP address 192.168.2.2
May 27 19:41:03 myhost pppd[3734]: Script /etc/ppp/ip-up started (pid 3739)
May 27 19:41:03 myhost pppd[3734]: Script /etc/ppp/ip-up finished (pid 3739), status = 0x0
I'm guessing that "Cannot determine ethernet address for proxy ARP" is my problem, but I can't find anything through Google that tells me how to fix it.