So you agree that a 'true Christian' will demonstrate some evidence of that love being in them?
Yes, believe this absolutely, though people are at different places in development, being a Christian not being free of possibilities to sin, therefore a Christian can be unloving at times. Like your caveat "some evidence" for this reason. But I believe, and has been my experience, a Christian grows in sanctity over time, is led and disciplined by God, of course the Holy Spirit the power of God and not impotent in the life of a true Christian. (Scripture even speaks to the Lord's chastisement of His children in Hebrews 12. A true Christian learns and grows, one way or another.)
It's a fundamental question, to my mind, how anybody of the Spirit can fail to have evidence of the Spirit. From what I see there are many fake Christians, of some unrepentant religion they call Christianity, but showing no real signs of spiritual life, and you see this in lack of understanding of scripture, legalistic religious systems, as well as rancor, all over message boards. This is your proverbial "faith without works is dead," which has nothing to do with works salvation, rather a true Christian will show some evidence of being Spirit-filled. One preacher asked his congregation, "If you were accused of being a Christian, would there be enough evidence to convict you?" If not, it's time to evaluate whether one is even saved.
Galatians 5
16 This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh.
17 For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would.
18 But if ye be led of the Spirit, ye are not under the law.
19 Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness,
20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,
21 Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God.
22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,
23 Meekness, temperance: against such there is no law.
24 And they that are Christ's have crucified the flesh with the affections and lusts.
25 If we live in the Spirit, let us also walk in the Spirit.
26 Let us not be desirous of vain glory, provoking one another, envying one another.