Do I Sound Gay? Film-maker's personal journey explores the 'gay voice' | Film | The Guardian
So, an entire documentary has been made by a gay man about the "gay voice". Looking at the trailer for it (it's in the article linked), it seems an earnest effort. Perhaps too earnest.
I think I have written here before that the topic is of interest because I once shared an office with a gay guy, who was surprised to learn that I could readily tell when he was taking a call from a gay friend. Not one with a terribly masculine inflection at the best of times, his voice clearly became "gayer" when he took calls from certain friends. As his sexuality was a potential issue for his job (we're back in the 80's now),he was concerned that his voice gave him away.
It's unclear whether the documentary offers any clear explanation as to how the stereotypical gay accent developed (and develops in individuals); as far as I know there is not really one simple answer.