Eaton fuller won’t go into reverse gear after broken reverse light switch

Have you got the new switch so you can cy how deep its safe to drill then buy a easy\/out then use a wrench on it to get a good bite with it and it should come out.

 

I would have to thank that if people were just driving the truck and not working it something internal would have to have happened in order to break the switch. Possibly the shift fork is bent. That could allow the shift fork shaft to travel further than it should. The reverse switch could cause it to bind because because it exceeds it travel limit in the detent shot.
Use a bar to shift it with the tower off and the switch out. Does the work?

 

Did you get the ball out of the old switch out of the hole the backup light threads into?

 

I suspect that is your issue. Take the new switch out and see if it will come out with a magnet.