it's like the dildo. when you go home and "relief yourself" it'll be an available option.
I tried and... nothing. did you need low sanity or something?
late response--- no, nothing special.i simply collected all of the chibi's, consumed them and received the idol.
hopefully you figure it out :(
"Relief yourself" works only when you have high libido. There's no other requirement then keeping the statue in your inventory when doing that at home.