The Dreamhold/WMG

You're not actually the grey-haired wizard.
Warning: Spoilers for all 3 endings!

Instead, you are a celestial being who was trying to stop the wizard from getting too powerful, knowing far well how dangerous he was to entire armies. In the drawing ending, the voice isn't talking to you, so you are instead overhearing the conversation between the wizard and the memory of his wife. In addition, "the stars welcome you home" in the Doorstep to Heaven entrance, which seems to indicate that you were there originally all along. The wizard likely worshipped you, hence the mural in his laboratory.

However, when you tried to chase him into the Drawing World, you failed to write the diagram and lost your memory and power. Through the masks, you ended up getting the wizard's memories and likely his personality and power as well.

The various clothing items and the string were look-a-likes to make the other celestial beings recognize you from a distance to pick you back up. You didn't know that would work, however, due to your lost memory, so you just looked at the mural and assumed that it was important, and it happened to work (at least if you are doing the third ending).