Some FG teachers say that a new believer must believe in Jesus specifically FOR the purpose of receiving eternal life.
Other FG teachers say the new believer must believe in Jesus’s finished work, and they will receive eternal life as a secondary result of that belief.
In my estimation in both cases the person who is believing is aware that the end result will be the reception of salvation. It seems that those who believe must understand and agree that Jesus gives salvation either directly or as a secondary result of belief, so I think both are technically believing in Jesus for a reason. The reason is so that they can have everlasting life/salvation/justification.
Some who teach “believe in Jesus FOR eternal life” argue that 1 Timothy 1:16 proves that we need to believe in Jesus FOR eternal life. This is a difficulty because it’s the only verse in the Bible that uses that construction, and the construction does not appear in the Gospel of John which is specifically evangelistic in the first 12 chapters. It likewise doesn’t appear in any of the other identifiable evangelistic passages. So, I don’t believe 1 Timothy 1:16 offers a conclusive end to the debate.
There are other teachers who prefer sharing the gospel from Paul’s writings where he emphasizes justification, forgiveness, salvation, and righteousness. I’m confident that a faith-alone salvation message can be drawn from these passages as well.
So, while it is my preference to use the phrase, “believe in Jesus FOR eternal life,” in addition to other explanations about the gospel’s broader context. I think that those who do not use the phrase have a strong Biblical argument to refrain from that terminology. It’s my opinion that even in cases where teachers use the Pauline focus of justification, the implied result is still eternal salvation. So, I do not intend to divide from other free grace believers who use a different approach from me.
Jesus told those who sought to kill Him, "But you are not willing to come to me that you may have [eternal] life." John 5:40. In John's Gospel, to "come to" Jesus means to believe in Him. See John 6:35 ("And Jesus said to them, 'I am the bread of life. He who comes to Me shall never hunger, and he who believes in Me shall never thirst.'"). And another way of saying "that you may have" is "for." For example, if I said, "I am going to the store FOR groceries," it is the same as if I said, "I am going to the store THAT I MAY GET groceries.
So, stated another way, Jesus told those who sought to kill Him, "But you are not willing to believe in Me for eternal life."