Your “I do however see” part is what I am talking about 
That is why I’m testing these things myself before posting them. Please just look at both Example Projects (FirstPerson, ThirdPerson) and you will see the difference in Mouse and Movement.
- With the ThirdPerson Character you rotate the Character by movement and the Camera by mouse. Therefore there is no strafing and running backwards.
- With the FirstPerson Character you rotate the Character by mouse only. So the movement is really just about movement and allows strafing and running backwards.
Initially I just wanted to give you the camera switch solution (“Then 0” execution wire) only, which would have been a screenshot from within my actual project (where i do not change movement like in Car-Perspectives). But I know there are always some more things happening in different situation, where I can help out too.
So what you want to do is just to switch between settings configured in both Characters of the Example maps. Or you customize your movement to allow running backwards in ThirdPerson as well.
I’ve tested the FirstPersonCamara at position 0,0,0 in first place, so you will see the hands left and right of you cam. Everything should be fine.