If you connect a 1kΩ resistor in series with your multimeter (*1), with your multimeter switched to the 20mA (or equivalent) DC current range, you can measure the ability of a logic circuit to source or sink current. And therefore work out if the voltage on an otherwise unconnected input is due to a pull-up (or pull-down) or is just a bit of small leakage current via the internal circuitry.

Use any two small diodes (preferrably Schottky, like BAT54 or similar) and two resistors like 4k7. Pull up both RxD inputs with resistors to their own power supplies, connect diodes' anodes to RxD inputs, cathodes to the other parties TxD outputs. That's all.