At the end of Who Framed Roger Rabbit Eddie asks Roger to read his love letter out loud, when Roger does we learn Marvin Acme's will was written in disappearing ink on the same piece of paper. It seems Eddie knew this- but how?
Eddie knew that Acme had a will (it was seen in the newspaper photo), Roger admitted he in the fit of jealousy wrote a love poem. In that scene is the hint, Eddie ask "old lipstick on mirror routine?" and Roger says "lipstick? yes. Mirror? no. I found thins nice clean piece of paper".
Now it was Marvin Acme who sprayed Eddie in the Club with invisible ink. So Valiant just connected the dots: In the club, where Acme used his invisible ink, there was a will written by him. Later on in the same club Roger find clean piece of paper to write on. It was a club, not a supply store so very unlikely there were two sheets of paper laying around. So that one found by Rabbit must been the will.