This is an interesting post. IMO - it seems like there's no partition there for two reasons:
1. That day was full of light so you'd expect some kind of reflection off of that glass. I just watched the parade film and it's quite unusual that nothing really stands out.
2. Here's a photo that I found interesting:
Connolly has his hand resting on the seat back or what appears to be where the glass would be. And there is no glare or reflection at all in that photo off of that glass if it was there.
Here's another pretty good photo - appears that there's no glass there.
But of course Jackie Kennedy said it was there so who knows?