I haven't found anywhere that explicitly mentions this, so I wanted to let everyone know that you can use a Raspberry Pi to connect to your router's serial "port" (pins). The Raspberry Pi's serial UART works with 3.3V, which is which most routers seem to use (you can't use an Arduino Uno, on the other hand, since it uses 5V).
You don't connect the VCC (3.3V) pin of the Pi to the router, but the rest are connected in the logical manner (GND<-->GND, RX<-->TX, TX<-->RX).
See here for the Pi's UART pin layout: https://pinout.xyz/pinout/uart (the short answer is that you will be using pins 6,8,10).
(Note you will also most likely need to solder pins on the router's PCB.)
Once you have everything connected, ssh into your Pi and use your favorite serial console program on the Pi (dterm, minicom, screen, etc) to talk to the router.
This configuration has the bonus advantage of being able to connect to the router's console "remotely" like a "tip line" (if anyone remembers what those are).
I know those USB serial dongles are dirt cheap, but you might not have one, and you might not be able to afford having a bricked router while you wait for your 50cent dongle to arrive from aliexpress.