I don't think so, but if anyone knows a data source it would be great.

It's so frustrating. As you say, the times at the station are accurate, but the Google data and NJ transit app aren't right.

Edit: After looking at the NJ Transit website, it seems pretty clear that they don't expose this data:

• Departure vision API's list of stations is just the rail stations, not light rail: https://www.njtransit.com/users/developer-tools. This also matches what you see under departure vision in the NJ transit app
• MyLightRail mentions that it tells you when the next scheduled train is coming, while MyBus says it has real-time information: https://www.njtransit.com/mybustexting
• Google/Lyft don't have the live time

I'm going to file a request ticket with them to expose this data, but presumably there's some reason they haven't so far