I’m no expert but I’ve had a fair bit of experience as a client and occasional student. You’re more than just your Sun sign (sometimes called star sign). You’re also heavily influenced by your Ascendant (or Rising sign) and your Moon as well.
This is why you can read Sag and think “that’s not all that accurate.”
When you know your exact birth time, a qualified astrologer will freak you out with specifics from your life up to the current time. Offering known (to you, not them) information is a sure way to convince you.
I’ll be writing a piece about this at some point. Shall I tag you when I do? No pressure if you’d rather I don’t.