Coming out can be a well scary process. She wants to be accepted for who she is regardless and you seem to be a very supportive friend which is great. Just continue to do what you are doing - she will see that you are sincere.
I had a similar situation. Turns out that she was hoping we might connect in that way since we were such good friends. We worked it out fairly simply once I realized what was going on. I just told her she wasn't my type in a friendly funny way. Lol! She remains my friend to this day.
Just continue to be her friend, as you have been. She'll realise you're still there for her.
Don't treat her any different than before, otherwise you don't need to do any convincing, she might just have a chip on her shoulder and will see your convincing as a negative thing.
You are a strange person. You say "you don't care" & then turn around and ask how you convince her that you don't care. That means "you do care", even though you really shouldn't. However, since I do not care ( for real ) whether you do care, or not, I'd say to hell with it, and let her think whatever she wants.
If she doesn't believes you, then Maybe she loves you and wants you to know about her feelings.<br />
Talk to her ;)
just be a loyal friend. she'll figure it out eventually
Just be there.
Just don't change your attitude towards her. She will begin to realize you are sincere.
Don't mention her séxuality unless she brings it up.
just carry on as normal & ignore the fact shes lesbian
She is trying to convince you to get sexy with you. .. shock her with a story true or not about you and a sexy male!... She just wants to have your undivided attention!
Get a boyfriend to prove that you don't care.