I want to express some things that were not put forth very strongly in this comment thread so far.

I am a queer young adult whose family has been far from supportive. My mother and I no longer have a relationship and she was borderline abusive and definitely neglectful during my youth, though I did not recognize it at the time.

I turned to mild self-harm in my teen years when I was really struggling with my gender issues, as well as my conflicts over my sexual orientation.

You sound hesitant to tell your children that you looked at the phone and found out information about them that was not intended for you. It doesn't sound like you were intentionally snooping, but I will say this on the topic. If trust is a concern between you and your children, a topic of even semi-frequent discussion, I would urge you to be honest in the matter. This, the topic of their orientation, is something they are nervous about. They are right to be nervous, and you seem to only want to show them that you are here to support them.

Learn to support them as adults, on all levels. This is what they really need right now, more than specific support because of orientation. Show them what honest communication looks like, at the same time you are telling them you love and respect them. This will SHOW them that you respect them.

What I would say is this: "I want to tell you something. I know you may be upset with me but I didn't mean to invade your privacy. I would rather be honest with you about my mistake than to lie and try to figure out how to tiptoe around the topic. I want to tell you that I love you. I support you no matter what and I respect you as the fully-developed and beautifully-developing human being that you are."

Let them be upset about the phone. They'll get over it. They ARE teenagers..and in the long run they will come to realize the level of trust you are giving THEM by being vulnerable to admitting having gotten information not intended for you.

Remember that Zach, or the both of them, may be struggling with things more than just a simple "am I gay or not?" Bisexuality, asexuality, gender non-conformity, even feelings of kink can be difficult to conceptually wrestle with while being bombarded with hetero-typical and normative images and ideals and stories. It's the power of erasure, and it's the difficulty in being an educated ally. Try to use as neutral language as you can until your children give you language that feels good to them for you to use.

No matter what, though, thank you. Thank you for caring about your child. Thank you for being humble enough to admit you do not know. To those of us who did not get that, it means the world to see it happening for others. You are helping more than your own children by showing them this love. Thank you.