Wow that was helpful thanks! In the end I found My modem's local IP is 192.168.9.1 and I can wget this call without logging in to the modem:

192.168.9.1/api/device/information, which replies with:

<?xml version="1.0" encoding="UTF-8"?>
<response>
<DeviceName>K4203</DeviceName>
<SerialNumber ...

I need to read the sim ICCID of the sim card from the modem. I can do it with one of these commands:

AT+CCID or AT+ICCID

However, I cannot get the modem into serial mode (I never see any /dev/ttyUSBx devices, before or after switching). It seems the command I use to switch from CDROM mode:

usb ...

I got another ZTE modem that works the same today: 19d2:1405

When it boots up, it auto-switches without needing usb_modeswitch, and it creates the eth1 port where the previous modem created the USB0 port:

from dmesg:
cdc_ether 1-1.4:1.0 eth1: register 'cdc_ether' at usb-bcm2708_usb-1.4, CDC ...

Update:

The modem switches on an ethernet port named usb0 without usb_modeswitch and without sending the AT commands (wvdial)

To get it working, I just had to add these lines to /etc/network/interfaces:

Yes, this is a raspberry, running ubuntu 14.04 and not raspbian. It was working perfectly (using usb_modeswitch) with my older Huawei modem while developing, but unfortunately I can't take the older modem into production - I need this ZTE to work.

Thanks for explaining the three modes of the ZTE ...

mmmm ok here is the output from dmesg:

[12841.145590] usb 1-1.4: USB disconnect, device number 6
[12841.145871] cdc_ether 1-1.4:1.0 usb0: unregister 'cdc_ether' usb-bcm2708_usb-1.4, CDC Ethernet Device
[12861.570381] usb 1-1.4: new high-speed USB device number 7 using dwc_otg
[12861.663132] usb 1 ...

This is a new modem from Vodacom South Africa. It is not is the database yet.

I tried getting it to switch but it doesn't. It has never switched out of storage mode, so I don't know what the target mode will be - I took a shot in the dark that it will be 1049 or 1050 but this failed. I assumed ...