It's not uncommon for UARTs to be done over 3.5mm audio jacks. Three wires (GND, RX, TX) is often enough. If the connector is no-longer there you can bypass it and tap wires onto the PCB yourself.
First you will want to grab a multimeter and measure the voltages of each wire compared to a known ground in the unit (whilst it's on). This will tell you which wire is GND and what the signalling voltage levels are (proper RS232 or lower voltage). RX and TX are typically both held 'high' to a voltage through internal resistors.
When it comes to working which way around RX and TX are: often you have to guess. To avoid potential damage put some resistors (eg 1Kohm) in series.