It's complicated and wonky but I would argue that you can't.
1.what is exactly the EOtG?
Warscroll tells us: It is a single model crewed by a skink priest ... - > points to the stegadon being the engine BUT
2. (marked in yellow) The stegadon bearing the engine - > reveals that the engine is a construct, carried by a stegadon and carrying a skink priest - > thus the attacks of the stegadon are not the attacks of the engine.. BUT
3. the warscrolls name is Engine of the Gods, thus the whole model is an EotG and bears all its keywords - > it is a hero - > it can have an item BUT its mount cannot.
4. Unlike every other mounted heroes, for example a Lord-Celestant on Dracoth, the EotGs Description does not fit the standard of a hero on a mount. It is, kind of, a mount of itself (plz someone draw an EotG mounting another EotG or itself! XD)
5. It comes down to the question of how we define mounted heroes exactly, bc tbh the skink priest is more of a passenger right now.
6. I hope you all get now, why I said this is a wonky situation...
7. In comparison to the stegadon which can (but does not have to) carry a skink alpha and lacks the hero keyword, the EotG always carries a priest and the actual engine around and has the hero keyword I would argue to define a mount which is carrying a hero as a mounted hero and thus deny the Stegadon to get any weapon artifacts.. Give it ignax's scales or something