Is there any indication in the Bible (N.T. is preferred) that the spirit of man can be discerned properly from the words that he is speaking? And is there any indication of the opposite - that the spirit of man can be easily discerned without listening to his words?
We know that "out of the abundance of the heart, the mouth speaks".
However, being able to entirely determine the state of someone's soul via their words is a talent not entrusted to [most] people (the exceptions being accounted-for in the Bible with the Apostles).
A period of witnessing all of the components of a person's life - words, actions, approaches to living, etc - would be needed to make a credible decision as to whether or not they are saved. As a Christian, it should be our goal to become more and more like Christ every day, and part of that IS with our words - "Let no unwholesome word proceed from your mouth, but only such a word as is good for edification according to the need of the moment, so that it will give grace to those who hear."
Indeed, this practice is followed by many churches when they have a waiting period between when salvation is professed, and when the believer is baptized.
However, even knowing all of that, we are still fallible humans, and there will be "Many will say to Me on that day, 'Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many [a]miracles?'"
Ultimately, it is only God Himself who fully knows the heart.
From the words that he is speaking: By the Emotion and Attitude used when speaking There are two forms of Discernment. The first is the Discernment of (Good, Right, Function) and (Evil, Wrong, Dysfunction). This first type of Discernment is called Wisdom. So a definition one could give to the word [Wisdom] is "The ability to see the answer to the problem."
To Make One Wise
So when the woman saw that the tree was good for food, that it was pleasant to the eyes, and a tree desirable to make one wise, she took of its fruit and ate. She also gave to her husband with her, and he ate. (Genesis 3:6 NKJV)
The second is the Discernment of the Spirit. The spirit can be read by the the display of ones attitude and emotion. The spirit develops by faith that things of function or dysfunction are in God's plan, therefore wisdom is not necessary. For what need is their to determine of a situation in its dysfunction. If indeed that situation fulfills a function? Or alternately if a situation fulfills a function, trusting in that functionality, when other functions can be used to fulfill the same purpose? Therefore since the one who is in the faith does not eat of the fruits of the knowledge of good and evil. The Holy First Law of simplicity is completely fulfilled.
But of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die. (Genesis 2:17 NKJV)
What then is the display of those not eating the fruits of the knowledge of good and evil?
But the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness, 23 gentleness, self-control. Against such there is no law. (Galatians 5:22-23 NKJV)
What then is the display of those eating the fruits of the knowledge of good and evil?
Now the works of the flesh are evident, which are: adultery, fornication, uncleanness, lewdness, 20 idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath, selfish ambitions, dissensions, heresies, 21 envy, murders, drunkenness, revelries, and the like; of which I tell you beforehand, just as I also told you in time past, that those who practice such things will not inherit the kingdom of God. (Galatians 5:19-21 NKJV)
Therefore by the Emotion and Attitude used when speaking, one can determine ones spirit.
Without listening to his words: By if one hears the truth
We are of God. He who knows God hears us; he who is not of God does not hear us. By this we know the spirit of truth and the spirit of error. (1 John 4:6 NKJV)
The one in error has the focus on both Now and also the Imagination
The lamp of the body is the eye. If therefore your eye is good, your whole body will be full of light. 23 But if your eye is bad, your whole body will be full of darkness. If therefore the light that is in you is darkness, how great is that darkness! (Matthew 6:22-23 NKJV)