MacBook Pro (late 2016) not waking/sleeping properly

The sleep sensor from your description is a strong likelihood. This series uses a simple Magnet/Hall sensor setup. Within the lid is a rare earth magnet that when in the down state meets up with the Hall sensor mounted on the main logic board on the upper case side. It's located just above the USB-C ports along the edge. Here's an image of the logic board where I marked it.

Take a rare earth magnet sliding it across the uppercase palm area where the sensor is located. Does the display shut off as you slide it over it?

@shingle if your MBP A1708 has the 820-00840 logic board then your computer also has a right sensor which is placed on the audio flex. You can always check the voltage on J6600 pin 25 and pin 27. If you have 3V on those, your sensors are good. If you do not have 3V, they are not. If you then approach your sensors with a magnet, the voltages should drop to 0v. J6600 is in the middle of the board, right hand side on the bottom side. It should be enough to just remove the lower case.

Now if your board is a 820-00239 ( MacBook Pro 13" Function Keys Late 2016) then you will find that there are 2 dedicated hall sensors. Check J5250 and J5260. Pin 3 are the ones that show the 3V.

Of course do this only if you are comfortable with using a multimeter and checking components on a circuit board :-). Since we do not know what your skills are, this is to be considered as just another option.