So I'm almost there. Almost.
Inspired by some posts by Mr. Bloomquist, I managed to get my dumb terminal hooked up to the Omega2 through a null modem.
I'm able to send text to the terminal by echoing to /dev/ttyUSB0.
And I'm able to read text from the terminal by cating /dev/ttyUSB0.
But I'm having trouble figuring out how to route a full shell with login to the dumb terminal.
The closest I've come is by issuing the command ash >/dev/ttyUSB0 2>&1 from my shell connection over wifi. But this only echos what I type on the computer connected by wifi to the dumb terminal. It doesn't accept any input from the terminal.
I've tried to figure out how to also route stdin to the same ash session with no luck. But I know it can be done, as demonstrated in Mr. Bloomquist's photos linked above which show a login prompt on a C-64 and a TRS-80 100.
Is it simply a problem of not being able to figure out the correct shell command from the wifi connected terminal, or am I going about it entirely the wrong way?