And how, exactly, does one know if they have eternal life or not? One of the scriptural answers that I get to this question is the following...
I John 5:13
"These things have I written unto that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God."
...but is this REALLY an acceptable answer? IOW, people consistently fail to mention/discuss the "these things" that John had written unto us. Such things as our need to walk in the light as He is in the light (I John 1:5-7), keep His word (I John 2:3-5), love our brother (I John 2:9-11), love not the world (I John 2:15-17), etc., etc., etc. IOW, we have a part to play in this as well.
Anyhow, since you specifically mentioned our own righteousness, as if it's of no value whatsoever, then what do you do with such verses as these:
I John 2:29-3:10
"If ye know that he is righteous, ye know that every one THAT DOETH RIGHTEOUSNESS is born of him. Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not. Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. AND EVERY MAN THAT HATH THIS HOPE IN HIM PURIFIETH HIMSELF, EVEN AS HE IS PURE. Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law. And ye know that he was manifested to take away our sins; and in him is no sin. Whosoever abideth in him sinneth not: whosoever sinneth hath not seen him, neither known him. LITTLE CHILDREN, LET NO MAN DECEIVE YOU: HE THAT DOETH RIGHTEOUSNESS IS RIGHTEOUS, EVEN AS HE IS RIGHTEOUS. He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil. Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God. In this the children of God are manifest, and the children of the devil: WHOSOEVER DOETH NOT RIGHTEOUSNESS IS NOT OF GOD, neither he that loveth not his brother."
???
"...every one THAT DOETH RIGHTEOUSNESS is born of him."
"Little children, let no man DECEIVE YOU: HE THAT DOETH RIGHTEOUSNESS IS RIGHTEOUS, even as he is righteous."
"...WHOSOEVER DOETH NOT RIGHTEOUSNESS IS NOT OF GOD..."
Are you telling me/us that you don't DO RIGHTEOUSNESS? If so, then...
God has given us all things which pertain to life and godliness and we need to use them. In doing such, we purify ourselves, even as He is pure.