Not sure what the "little round lights" are. Post a pic. But if they are coax cable, then they likely go to each room for watching TV.
To trace the speaker wire (your pic), go to home depot and buy a signal tracer. You clip the transmitter on the end of the wire you are holding (after stripping off the insulation) and then use the receiver to wave back and forth listening to it's tone to determine which direction that wire goes. Ultimately you will find that wire's end. Mark both ends with a wire marker (Dymo or other).
You will then want a whole home audio matrix (Russound / Nuvo) and audio sources (streaming and/or local media) that would be mounted in that closet. Is there a power outlet in the closet? That would make it much easier.
To trace the speaker wire (your pic), go to home depot and buy a signal tracer. You clip the transmitter on the end of the wire you are holding (after stripping off the insulation) and then use the receiver to wave back and forth listening to it's tone to determine which direction that wire goes. Ultimately you will find that wire's end. Mark both ends with a wire marker (Dymo or other).
You will then want a whole home audio matrix (Russound / Nuvo) and audio sources (streaming and/or local media) that would be mounted in that closet. Is there a power outlet in the closet? That would make it much easier.