A very Weird Glitch with the mod "Precision Aim" causes this problem. If you don't fix it then sooner or later this will cause a problem with your other missions as well. This Just Cause 3 Guide will help you with the Trick which will fix the Homing Missiles Issue.
You need to access your Mod Menu as the main cause of this problem is the Mod - "Precision Aim". If you deactivate this mod you will not be able to lock onto objects with any homing missile-type of weapon. This Below Fix is a Temporary Fix as we too are waiting for the upgraded Mod. It might take hours to fix, but you are luck it will be fixed at once.
Step 1:
Exit your game normally
Step 2:
Deactivate the mod "Precision Aim"
Step 3:
Restart your game
Step 4:
Enjoy homing missiles
Note: Avoid trying this change with the game running in the background.
If you have any doubts with the Missiles or any other issue with Just Cause 3 do let us know in the comments below.