I'm not sure what you mean by chip model or how to get anything about the chip except USB ID (when hooked up to regular PC, or in the stock-mofi-firmware lsusb in my OP).
As for brand and model of cable, I actually have 5 of these, 4 appear the same (one of which is the one I've been using up to now), about 6" long with no distinguishing marks, just a "Q.C. OK" + bar code + serial number sticker, and one is different, about 24" long, with sticker saying:
USB-RS-232 Converter
Model: USA-FTDI-A36
Data Communications
(bar code)
(serial number)
All 5 of them show exactly the same in lsusb when connected to a regular PC.
The FTDI chip the cable uses has a model # which denotes what driver it will then need, as FTDI makes a range of chips for serial communitcation.
A quick search of the model # (USA-FTDI-A36) shows you're likely using a cable with a FTDI FT4222H chip, of which requires the D2XX drivers
It appears you have all the correct FTDI/serial packages installed, except for libftdi or libftdi1, unless either was installed as a dependency and not listed in your output... please post the output of: opkg list-installed | grep ftdi
As the USB core is not even enumerating devices when they are plugged in, the choice of a high level driver is irrelevant.
The 305X chip's USB module contains "On the Go" logic so it can operate as either a host or a device. This is common on smartphones so the user can either connect the phone to a PC as a device, or use it as a host to access a memory card, etc with the phone OS.
Only host mode is possible the way that routers are wired.
Okay thanks. So noting in my OP that (with the OEM provided firmware) the message when USB devices were connected was:
[ 429.090000] usb 1-1: new full-speed USB device number 2 using dwc_otg
and googling there does seem to be an older (12.09 timeframe) openwrt package kmod-usb-rt305x-dwc_otg (no longer supported? as its not in the current releases or downloads folder) but this prodded me to list available packages mentioning "otg" (which found none), and "dwc" which found kmod-usb-dwc2 and kmod-usb-dwc3.
root@OpenWrt:/# opkg update
...
root@OpenWrt:/# opkg install kmod-usb-dwc2
Installing kmod-usb-dwc2 (4.14.63-1) to root...
Downloading http://downloads.openwrt.org/releases/18.06.1/targets/ramips/rt305x/packages/kmod-usb-dwc2_4.14.63-1_mipsel_24kc.ipk
Configuring kmod-usb-dwc2.
[ 241.945264] kmodloader: loading kernel modules from /etc/modules.d/*
[ 241.968572] dwc2 101c0000.otg: Configuration mismatch. dr_mode forced to host
[ 242.018950] dwc2 101c0000.otg: DWC OTG Controller
[ 242.028572] dwc2 101c0000.otg: new USB bus registered, assigned bus number 1
[ 242.042887] dwc2 101c0000.otg: irq 26, io mem 0x101c0000
[ 242.057925] hub 1-0:1.0: USB hub found
[ 242.076870] hub 1-0:1.0: 1 port detected
[ 242.104031] kmodloader: done loading kernel modules from /etc/modules.d/*
root@OpenWrt:/# ls -latr /dev/ |tail -n 5
crw------- 1 root root 108, 0 Dec 5 19:23 ppp
srw-rw-rw- 1 root root 0 Dec 5 19:23 log
drwxr-xr-x 3 root root 60 Dec 6 15:13 bus
drwxr-xr-x 4 root root 1200 Dec 6 15:13 .
crw------- 1 root root 4, 64 Dec 6 15:14 ttyS0
(connected USB-RS232 adapter here)
root@OpenWrt:/# [ 270.286555] usb 1-1: new full-speed USB device number 2 using dwc2
[ 270.557682] ftdi_sio 1-1:1.0: FTDI USB Serial Device converter detected
[ 270.571403] usb 1-1: Detected FT232RL
[ 270.603772] usb 1-1: FTDI USB Serial Device converter now attached to ttyUSB0
ls -latr /dev/ |tail -n 5
srw-rw-rw- 1 root root 0 Dec 5 19:23 log
drwxr-xr-x 3 root root 60 Dec 6 15:13 bus
crw------- 1 root root 188, 0 Dec 6 15:14 ttyUSB0
drwxr-xr-x 4 root root 1220 Dec 6 15:14 .
crw------- 1 root root 4, 64 Dec 6 15:14 ttyS0
(note the chip model actually appears to be a FT232RL from the message above)
Hot diggity, thank you everyone who suggested things here.