Mental activity is worthless.
Only obedience matters.
Believe "pisteuo" does not mean obey. Believe means have faith in/trust in/reliance in. Obedience which follows is WORKS. The Greek words for "pistis" and "pisteuo" are two forms of the same word. "Pistis" is the noun form, "pisteuo" is the verb form. Nothing in the root meaning of either word carries any concept of works. If you believe in/have faith/reliance in in Christ unto salvation, then you are trusting in Him alone to save you. This belief results in actions appropriate to the belief (to one degree or the other/all genuine believers are fruitful, yet not all are equally fruitful) - but the actions are NOT INHERENT in the belief.
Demons believe, but they obey Satan.
In James 2:19, we see that the demons believe "mental assent" that "there is one God," but they
do not believe/
have faith/trust in/reliance in Christ for salvation. In other words, they do not believe on the Lord Jesus Christ (Acts 16:31) and are not saved.
Their trust and reliance is in Satan, which explains why they obey Satan rather than Christ, as demonstrated by their rebellion in heaven and continuous evil works. The word believe "pisteuo" can describe mere "mental assent" belief, as in James 2:19, or also include "trust and reliance" in Christ for salvation, as in Acts 16:31.
He who believes in the Son has eternal life; but he who does not obey the Son will not see life, but the wrath of God abides on him.” John 3:36
I often hear works-salvationists (especially Roman Catholics) quote John 3:36 in the NASB and "stress" the word "obey" to imply that we are saved by obedience/works. In regards to "does not obey the Son" in the New American Standard translation of the Bible, this does not mean that receiving eternal life is received based on the merits of our obedience/works which follows believing in the Son, but
obey by choosing to believe in the Son. If John wanted to make obedience the central theme in salvation here, he would have said: "He who believes
and obeysthe Son has eternal life," but that is not what John said. To obey the Son here is to choose to believe in the Son.
The King James Version renders this same verse as: He that believeth on the Son hath everlasting life: and he that "believeth not the Son" shall not see life; but the wrath of God abideth on him. The NIV says "rejects the Son"and the CSB says, "
refuses to believe in the Son." The Greek word translated as "believeth not" in that verse is apeitheo and it means: "not believe, disobedient, obey not, unbelieving." Strong’s definition of apeitheo is "to disbelieve willfully and perversely."
In the context of 3:36, to "not obey the Son" means to reject the Son by refusing to believe in the Son.