"...reply to questions under partial oath and after a statement of pertinence has been made"

According to Robb, this term referes to an oath referring to only part of a case; by which it could be assumed that the person would be testifying only to some of the facts thereof, but not all.

An "oath as to part of the facts only" could be a more specific translation if the context does not allow this to be explained further.

juramento indecisorio - testimony that is weighed by the judge against the party's other evidence

Spanish-English Dictionary of Law and Business (Thomas West)

Trabajo como interprete judicial en los tribunales de Illinois, esta clase de testimonios se toman cuando, a pesar de los hechos, el juez toma la ultima decision, pudiendo o no tomar en cuenta el testimonio, aun cuando haya sido tomado bajo juramento.

according to contents of testimony it will be the judge who will decide of it is valid or not