When I was 12, I would not have discussed what I was feeling sexually with my parents, but that was in 1969. Life was different then. The church was a different place. I would not even have discussed SSA with my parents at the age of 20. Mine was a Christian home and while I knew that they loved me, my perception was that even feeling such things would get me thrown out of the house and the church. That may not have been the case, but there was certainly a air of conditional love when it came to such things. But I digress.
The things that parents and children discuss today are all over the board and nothing is off the board. If your child or young adult confesses to you that they think they are gay or lesbian or same sex attracted, then you have certain responsibilities that you must observe. Love them. Accept them. Do not approve of the sexual behavior. Indeed, there may be no actual behavior to disapprove of. This is why you love them and endeavor to stay in their lives. Never let them forget where they came from and that, whatever else happens, you and Jesus still love them. Lives and life circumstances change. People change their minds. People change. Some things like love of Jesus, family and church can override a desire for sinful things. It happens. Pray, love and accept. Let Jesus do whatever else may be needed.
What you want to avoid are angry, divisive conversations that will separate you from the one you love. This is no time for conditional love on either side of the discussion. Do not burn bridges. Always leave the door open.
Many times we look for someone to blame. Parents will doubt their parenting skills. The SSA young person might blame them or even God for what they perceive they are becoming. This needs to be minimized or put off the table completely. No one knows why any one is gay. At the point where it is being talked about, it's really not relevant anymore. Everyone just needs to start the conversation where they are at. It is no time for recriminations.
You say, "but what if they choose to live gay?" I would say first, this may not be a forever type decision. It is possible to turn back. It is possible to decide to live celibate. It is even possible to explore heterosexual marriage. NEVER close the door to any possibilities.
Second, if they do not do those things, love them anyway. Do what Jesus would do. Pray, love and accept them as your children and as people that Christ loves. Let Jesus handle it once your possibilities are exhausted.
People make choices. Some of those choices are bad and some are downright self destructive. That can be minimized with love.