Just wanted to update here. I was able to disable the F1 speaker issue, but the trainer never did activate.
Sounds like something may be blocking it. Make sure to turn off your Firewall and virus program. Extract the Trainer to the Steam/Tomb Raider folder and run both game and Trainer "as Administrator."
I just finished the game and then did a little Camp Fire bouncing and the Trainer worked just fine as per instructions.