No reverse and no backup lights activating?

The truck listed above is an FX4 5.4L Triton. The transmission Fluid level good and coloration/texture is good. Gear shifter and indicator work properly, no faults. Shift to reverse and does nothing as if went to neutral, no bump, no feel of trying to engage or anything. Press accelerator and engine just revs up like in neutral. Does not feel as even trying to engage at all. All other gears work and shift smoothly without any faults. No DTC codes on dash. Manually put in 1st and works without any faults. No vibrations, no hard shifting, no noises, no stalling nor any shuttering, idles smoothly even with shifter still in reverse and seems not to be of any lack in power nor acceleration in any of other gears going down road. Downshifts smoothly with hard acceleration as expected. Have noticed that backup lights do not come on when shifter is put in reverse. Seems as linkage is working properly and is free of any bind or restriction. Trans position sensor, would it cos both of the faults, no reverse and no back up lights to activate?