What a great research discussion this is!
(until it went silly)
My vision to these mysterious circles is quite different from all of your suggestions.
I believe its a 19th century mistake, a free style artist's interpretation by Jean-Francois Champollion back in 1835.
The circle Is nothing. Copied again and again by illustrators and sculptors. Its probably based upon the image of an Egyptian hole
So lets trace this thing back.
Wiking wrote: I think only the sculptor of Cäsar know it.
I think he doesn't.
He must have copied it from the Osprey Books:
The Osprey illustrators copied it from Jean-Francois Champollion:
Jean-Francois Champollion, founder of Egyptology, copied it around 1835 from the 13thC BC Ramesseum in Egypt:
So here something went wrong. The original does not show any discs at all.
Neither do all other Egyptian or Syrian reliefs depicting Hittite chariots:
Why did Champollion add those discs?
Maybe because he wanted to decorate the plain sides of the Hittite Chariots.
Where did he get the inspiration?
Maybe here:
Many Egyptian reliefs show Egyptian chariots with small circles similar to 'our' discs. These must be holes though. Most of them are situated in the back of the chariots sideboard. Probably to create a handgrip. Or a hole to attach ropes for quivers:
But some images show these holes a little more positioned towards the front of the sideboard.
These represent Egyptian chariots, but since Champollion was one of the first people to study them, he may have judged these as Hittite ones.
What is it? As I'll need to paint it, I have to know.
My advice to you: Take a knive and remove it from the chariot so your problem is solved.