Have you had a golden age already? One thing to remember is each successive age will require additional great people (that is, your second will cost you 2, your third will cost 3, etc). So if you've already had a golden age, and only have one great person, the option will be greyed out for you until you get a second great person.
Personally, i think the great people you get from tech are just like any other great people, so it should work....
Remember that to start a golden age that requires more than one person, each of the great people used has to be a different type. You probably already have the type of great person that the tech gives you.
Is the length of golden age time the same as for one?
It is. And for that reason, I'll rarely take 2 Great Person Golden Ages, and never more than that. Though if you run a specialist economy (I don't), Great People are more expendable.
I may not be the most efficient user of GP, but I mean in theory you could do like a what 5 person Golden Age? Three isn't overly hard. Four is tougher, but not unreasonable for late game.
How else are you going to change multiple civics??