No, it's not an elision - or not in the grammatical sense.

And I was wrong when I said it's not correct English. It's correct, but ambiguous: 'at home' could refer to the glasses or the forgetting. In practice it doesn't matter; most people would understand that they forgot their glasses and they're probably at home.

"I left my glasses at home" doesn't to me imply it was deliberate. Rather the opposite, but that's probably because glasses are often forgotten and left at home. Unless in a context such as "I couldn't bring everything. I left my glasses at home."

But I would assume "I left my car at home" meant it was deliberate.