CSX sold off the entire former L&N/Seaboard line from Pensacola to Baldwin (close to Jax), and it's run by the Florida Gulf & Atlantic Railroad now.
They're not putting in PTC, which is possibly a big reason CSX sold it off to start with, so you're not gonna see Amtrak east of Pensacola like all those lineside communities hoped they would.
The Sunset Limited was a joke through North Florida when it ran, as it was often many hours and late and hit key towns like Tallahassee in the middle of the night (putting off passengers in several places that weren't all that safe). If you saw the train stop on those stations along the Gulf Coast, you'd often see few (if any) passengers getting on or off.
After the '93 Big Bayou Canot wreck, I'd heard that Amtrak was wanting to kill this run, and hurricane Katrina gave them the excuse they needed (though strong lobbying forced Amtrak to put the service back as far as New Orleans).