It was made in Cycles and therefore everything was present and correct when imported into Cycles. I realise Cycles has been sped up with 2.8 - but it's still painfully slow to the point that, I use a render farm to handle my animation - which costs of course. I looked at a free render farm but it was hopeless.
It's certainly true to say I don't know how render engines work - therefore, I do wonder why the model looks SO different in Eevee. The HDRi didn't seem to register on the surface, the model was plastic looking - and the eyes of the model were either so dark you couldn't see them - or they weren't present. That said, believe I found a way to make the eyes appear in Eevee by switching their mode from Opaque to Multiply - or something similar. Before the 'dino-project' I animated a drone in Eevee - and absolutely LOVED how fast it rendered! Wow - I can do my own renders now - and not have to wait fifteen hours!
But then I imported the Cycles model and oh... back to paying for my renders. I hear 2.81 is happening in November and that there's an addition / update to soft shadows in Eevee - so I look forward to that. I've seen workarounds on how to create shadows in Eevee - but why do you have to use a workaround / hack? Why doesn't Shadow Catcher work in Eevee? Or rather, the option isn't there. So, as you can see - I don't understand how render engines work.
Then I had the frustration of not finding a way to make the floor plane transparent in Eevee - so even if I employed a shadow hack using fifty nodes (!) - I couldn't render without the floor plane.
I got really excited when I first used Eevee with a model NOT made in Cycles because of the incredibly fast render times - but I didn't need shadows at the time and the model looked right. I naively expected to import the Cycles velociraptor model, switch to Eevee, create transparent shadows and render myself in a style ten times faster than Cycles. Negative!