He, She, They, His, Hers, Theirs, His, Her, Their
I never was comfortable with the "he/she" "sir/madam" thing. When I went to school and was taught English things were simpler. We were taught that when speaking in that sort of universal "mankind sense, we were to use the masculine tense. "Mankind" meant everyone - men, women, children - not just adult males. It made sense. Just like it was Mr. Mrs. and Miss and there was no title for a young single male - young or old. I never thought it was fair that my sister might have mail written to Miss Gnomestead and my parents to Mr Gnomestead and Mrs Gnomestead but me only Darrell Wade. I guess there was always "Master" but who ever used that?
As I went through the school system and things in life and society changed - they brought in the metric system and feminism - somebody decided to fix the issue about "Miss" and that there should be "Ms". I thought, "Great, now not only is there Mrs for married women, Miss for single women, but now there is Ms for women who wish not to be known as either. For guys there is only Mr which I guess works for boys too.....
I guess I got over it. I'm not married and I happily use "Mr" - but there is still the issue of "he/she".
In some reference books they make a statement like "In this book we have decided to use the masculine gender..." or "...feminine gender..." and then keep with that gender for cases where there is no specific gender. I guess that is less cumbersome than the a/b method. A better way that I have found was described in the beginning of "What Colour is My Parachute" a book on career and job search. In that book the author explains that less important than gender agreement is number agreement and that often we will use the plural for singular incidents like in signs. For instance asking that "People not use their cell phones." "Their" is used whether referring to singular or plural in many such cases so in that book by Dick Bolles he uses the plural instead of singular gendered pronouns.
So instead of referring to "his book" I might refer to "their book" if I do not know the gender or if gender is unimportant. Or if the reader is uncomfortable with the use of "it" as a neutral gender pronoun for people I suggest they use "they" rather than "he/she".
I have tended to use this convention when I wished to write about someone without giving information about their gender so as to keep their identification even that much more anonymous.
An interesting situation I treat a bit differently is a matter of speaking of religious matter. I often prefer not to use gender when refering to God. I am Christian so I would refer to Christ as "He" and "God the Father" as "He", but the "Holy Spirit" I might not wish to give gender to. Also referring to God as a whole I prefer not to use "He", but I do not wish to say "She" and certainly not "He/She" and definitely not "It". So for me my solution is simply when referring to God, I try not to use a pronoun and instead simply use "God". So where I might use "He" or "Him" or "His" I would use "God" or "God" or "God's".
I am lead to understand that in Hebrew, at least older Hebrew, a special tense/gender or whatever you call it is used for God that is not a masculine form or a feminine form.
So when I write about my friend I will say that they are a good friend. You will not know what their gender is. I might also write to you that as a Christian I believe in God and that I do not typically refer to God's gender or use pronouns for God. Instead I will refer to God as God. For instance instead of saying "He created the World." I will say "God created the World".
Anyway, so in my writing I hope you don't get confused if it seems I might be mixing up my pronouns when speaking about singular people of undetermined gender.