Tam Kam doesn’t produce any male flowers for me.
I would recommend Coffeecake for @hambone That one produces over a hundred fruit every year and hasn’t taken a break for the past 3 years. It’s one of the tastiest kaki. Pair it with Cheong Pyong for excellent pollination. I think Threefold Farm sells scion of that one. Any kaki fruit in your yard would be seeded.
There is a hybrid male “universal” that is becoming more available. That might be the ticket for those of us in cold zones.
It is reputed to also produce delicious fruit.
Ram,
Does this male model 
have a name?
It’s called “universal’
Is it called Universal because it can pollinize kaki and virginiana?
Not sure of the reason for its name. It will definitely pollinate hybrids. And apparently has male/female flowers and fruit.
My grafts are small and I will only know in a few years.
Bohzy Dar is another that should pollinate all. It is a hybrid that has male, female and hermaphroditic flowers, which I think is also true of the kaki Cheong Pyong @PharmerDrewee mentioned.
Mine is still small and in a treepot for too long now, but seems fairly happy. It gave me 3 little fruit from hermaphroditic flowers last year, but only has one flower this year, which is either female or hermaphroditic. The flavor was good on the small fruit last year, but the female flowers should make larger fruit up to about 100g.
I believe the Ukranian growers prefer Universal for fruit. Bohzy Dar has the benefit of supposedly staying a fairly small tree.