The current that was drawn by the original lamps is not an issue.
The purpose of the series resistor that is used with the LED is to limit the current through the LED. The current will likely not be the same with the LEDs and that will be fine.
You need to determine the actual voltage present and determine if it is an AC voltage or a DC voltage.
Here is a link to one of many LED resistor calculators.
LED RESISTOR CALCULATOR
If it is an AC voltage and you only use 1 LED, you will need a separate protection diode to protect the LED from excessive reverse voltage.
By the way, according to what I found, it is DC 12v for the NAD back-light bulb.
If you are going to use 2 diodes you can connect the diodes in parallel, but opposite polarity. If you decide to do this, use the top calculator to determine the value of the resistor, but connect them like the bottom diagram, but reverse the polarity of one of the diodes. You will not need a separate reverse voltage protection diode in this application.
If you need more than 2 LEDs, you may use the middle circuit with a separate diode to protect the LEDs from excessive reverse voltage.
The separate diode would be connected in series with the LEDs.
A 1N4001 diode would work fine if your supply voltage is 12 VAC.
If the voltage present is a DC voltage, you will need to pay attention to the polarity, but you will not need the separate protection diode.
I just read my post and it is not as clear as I would like it, but it is my medications.
Anyone may feel free to add to or correct my post.