To add some more info to the other solution, I found the transmitter coordinates can show up in 2 different locations
1. On the south beach, just above the campfire.
2. On the elevated mesa as you head towards the eastern safe house with the crank in it.
The beach is by far the hardest location to clear out on this island, so maybe it's best to check location 2 first and get the crank first so you can make a hard save, at either the southeast or northwest safehouse.
I must've replayed this DLC on Iron Mode at least 5 times because I thought there was a bug when they didn't appear on the beach.