Would you use this form for any other type of sentence? Could you say something like:
"Ik ben overtuigd van uw eerlijkheid"
(I am convinced that you are honest)
Absolutely. The more literal translation of that would be "I am convinced of your honesty". The word "gelijk" doesn't have a good literal translation, the closest would be "correctness".
Ahh, thanks. The second I read your reworded sentence reworded it made sense to me.
A bit like the French vous avez droit
"Vous avez raison."
Of course. Thanks. Time to strengthen my French skills.
Why is (a form of) "hebben" not used here? Is it sometimes optional, always optional, or sometimes should it not be used at all?
That is possible, but less concise: "Ik ben overtuigd van uw gelijk" = "Ik ben ervan overtuigd dat u gelijk heeft". "[Someone]'s gelijk" is a way of indicating that that [someone] is right.