I have a '60 but changed to front discs years ago -- it is a disc/drum system though.
While I was doing my conversion I was told the late 60's Mustang master cyl is a dual mater cyl and will work for a drum/drum system. Might work for your application on a '62.
Not sure what length push rod.
A fellow who might be able to help and did the conversion on my booster is Booster Dewy @ Power Brake Booster Exchange. He will most likely know what length push rod. He's always been very helpful when I've called.
There is a super long discussion on the 58-60 forum about disc's and dual master cyl - might get some info there if you have a few days to read it.