Secrets of the Gallant

[ChaosMachine]

Could this work with a face down normal monster?

 

[LionHeart]

Your opponent would have no way of knowing whether or not it is a Normal monster, so I'd say no.

 

[slither]

As LionHeart stated, a face-down monster, has no stats, attributes, etc. it's basically a blank card (as it is unknown), so you can't use Secrets of the Gallant on a face-down monster.