Here's my take on a circuit (sim below) to do what you want, that avoids any concerns about how the LED circuitry is configured, and requires no ground connection between the indicator panel and the number circuitry.
It uses one opto isolator to detect the Room LED and one to detect the Bathroom LED, with outputs paralleled to a MOSFET that drives the number LED.
The circuit detects the signal across either the Room or Bathroom LEDs and lights the corresponding number LED.
(How much current will the number LED require?)
The yellow trace shows when the Room LED is on and the red trace shows when the Bathroom LED is on.
The green trace shows that the number LED is lit when either the Room or Bathroom LED is on.
The number power supply voltage is somewhat arbitrary and can be different if you want.
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