may a person has the right not to exercise his right as provided by the constitution?

Of course. Many people ignore their constitutional rights through silence.

if a person opted not to exercise his right, is he estopped to claim such right later on?

right to exercise or right not to exercise. the right to choose not to exercise the right is actually an exercise of a right but such is in the negative manner but it doesnt necessarily mean or follows that such right renounced shall forever not be exercised.

Art 6 of New Civil Code (RA 386) stipulates that rights maybe waived provided such act is not contrary to law, public policy, morals or good customs, or prejudicial to 3rd person with a right recognized by law.

Waiver must be clearly and convincingly shown either thru express stipulation or act admitting no other reasonable explanation.

However, regardless the person chose to waive his right, the State shall accord him full protection and the court shall see to it that his basic constitutional right is not disregarded.

Should the person decide to invoke his right, after waiving, specially if such in premised on consent given under a mistake or misapprehension of fact, he can do so.

maybe yes because there are constitutional rights that can be waived.