^ Where did you take this measurement? If between the driver board and LED array, I'd think your driver is failing.
If this is before the driver, something is very wrong because an incan bulb drive would not be PWM at all, would be continuous 12V, direct battery feed switched on through the fog lamp switch and a relay. Ford has been switching some circuits from the old style mechanical relays to more modern, transistorized relays, and if that happened by '16, that may be where the problem lies and so the next thing I'd do is try swapping that relay with another of same, transistorized relay... except it may not be plug-n-play swappable (see below).
However on the wiring diagram I have for a '14, it shows the older style mechanical relay, but it's embedded in the BCM so not so simple to swap out, and yet it certainly shouldn't be rapidly cycling to product PWM, would be constant on, or off. I am wondering if you are just measuring residual switching noise caused by the LED driver circuit, is there really not any DC voltage near 12V present? I mean your picture just shows ACV.
The correct replacement part for incan fog bulbs conversion to LED will necessarily have a driver (or at least a series resistor if a bad design), and still the input for that should be 12VDC through the BCM, not PWM till after the driver.
This is from the '14 workshop manual: