Welcome.
Assuming you are listening monophonic, The selector you are using is a (six pin) double-pole-double-throw DPDT that each 'pole' routes amplifier 1 or amplifier 2 towards the headphones.
That is, centre pin to headphones, one end to amplifier 1 and the other end of the same switch section to amplifier 2 output.
IGNORE the triangles and their lines above - image borrowed from the web.
Circuit should be altered to :
NC1 and NO1 are your amplifiers outputs 1 and 2 positives. Com1 is your earphone positive.
NC2 to LED1 one; NO2 to your LED2. Com2 to +3V. All negative common grounds together for earphone, amplifiers outputs and LEDs.
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Can be done also by replacing your 6 pin selector a with a 9 pin one that has an extra set of switches 3PDT triple-pole-double-throw for the extra set to drive the leds, plus, the 3V supply for them to lit.