We are going to have MORE fun with grammar! Yes, it is possible.
I have colorized the verb tenses in John 12.36 so we can see what John does here. Green marks a present tense in the Greek which is used for a continuous action; yellow marks an aorist tense, which is something that happened in the past which is not still going on. We like to think of this as a “snapshot” of something in the past.
So look what John does for us here. He weaves in some excellent theology in his use of verb tenses. You may become sons of light is an aorist tense, a snapshot of something that happens once. When we come to faith in Christ it is something that happens once, we do not need to keep coming to faith over and over again.
Look at what John does with believe in the light. This he writes in the present tense signifying something that is ongoing in the present, a continuous action.
The Holman New Testament Commentary points out how Leon Morris captures what is going on in vs. 36 so well:
Morris notes an interesting grammatical switch in this text. The words put your trust in at the beginning of verse 36 appear in the present tense, emphasizing continuous belief but become late in the verse occurs in the aorist, pointing “to a once-for-all becoming sons of light. While faith is an activity to be practiced without ceasing, one does not become a son of light by degrees. One passes decisively out of death into life (5:24)” (Morris, p. 601).
So much theology in such few verb tenses.