Started Dawnguard. Just about ready to go to castle/Soul Cairn.
-- Asked Sorine "what can I do to help." Did 5-6 Ancient Technology quests for all Crossbow designs up to final Enhanced Dwarven Crossbow.
-- Spoke to Isran. He told me to talk to Gunmar about how to help (those are just radiant quests so far) and Sorine about finding Crossbow designs -- I thought, uh oh, I already did that...
-- Now, when I ask any Dawnguard quest givers for quests, Gunmar gives me radiant quests, Florentius is having me track down Dawnguard enchanted weapons, but... Sorine:
A) won't progress into researching Bolt types as quests
B) she just refers me to the other guys when I ask how to help.
C) she has a quest marker on her head for Ancient Technology

Help... how do I get Sorine to give more of her own quests?

You can't do this quest again, because there's nothing else to unlock. More info:
[url=https://en.uesp.net/wiki/Skyrim:Ancient_Technology]https://en.uesp.net/wiki/Skyrim:Ancient_Technology[/url]

As explained above, there is a rare bug that the recipes may not be unlocked after completing the quest 6 times, in this case, you can use console commands to unlock the glitched recipes:

Thanks! But, I tried those console commands but got "Unknown Variable" as an error.

PS: I think this is a quest marker that PRE-DATES Ancient Technology. Isran tells you to go talk to Sorine and you get a Miscellaneous Quest marker on her... I think when you tallk to her the Misc quest is supposed to "complete" and Ancient Technology begins. So I believe I'm stuck there: Ancient Technology can't start because it's already complete.

Its a bummer you got that glitch but is it really worth the bother to you?

I've given up at this point. Was hoping for a console command but I can live with it.