Using a regulated current source to light them, wire the LEDs in series and short out the segment which you want to be dark.

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You can possibly use a buck-boost converter to make the 30V if you don't already have a suitable voltage.

Here's a simple way to build one using a LM2596S module:

 1. Remove the potentiometer and both large capacitors
 2. Connect one of the salvaged capacitors between +in and +out (positive to +in), and fit a 1uF ceramic capacitor where the output capacitor was.
 3. Connect a 100 ohm resistor from the -output to the centre potentiometer terminal.

Modified in this way, it will create a negative voltage on the -out terminals and act as a 12.5mA current sink at the centre potentiometer terminal (with source at +out) if power is applied between +in and +out.

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