When you suddenly remember you have a mustache and all of a sudden become paranoid everyone is staring at it; thus, stache-conscious.
"So I recently got this mustache and I keep forgetting about it. Then I remember I have it and feel like everyone is staring at me."
"Sounds like you're a little too stache-conscious. If anyone is staring at you, guaranteed it's because you're walking a cat on a leash."