The Greek eilikrinēs means sincere, pure, unmixed. The word's etymology is disputed but possibly relates to testing something in the sunlight (eilē + krinō) — holding a jar of honey or wax to the sun to check for impurities. Paul uses it in Philippians 1:10: 'so that you may be able to discern what is best and may be pure (eilikrinēs) and blameless for the day of Christ.' Peter uses it in 2 Peter 3:1 of sincere understanding.
The eilikrinēs character is one that can be examined in full light — no hidden impurities, no mixture of motives, no wax filling the cracks of cracked pottery (as ancient vendors would do to hide defects). The NT call to sincerity is rooted in the character of God, who is utterly transparent and undeceiving. The gospel creates sincere people: 'I urge you, brothers and sisters, by our Lord Jesus Christ and by the love of the Spirit, to join me in my struggle by praying to God for me' (Romans 15:30) — earnest, unmixed intercession. Sincerity is not naivety but integrity of motive aligned with truth.