the going theory for a while was that there was an additive put in the oil from the factory that would keep the tick away until the next oil change.
The tick in the video occurs at random time intervals, thus I doubt it to be mechanical in nature (such as missing cam teeth or loose rod bolts).
That leaves one to look at noise sources that are not periodic in nature such as devices that control fluids (oil, air or water) such as relief valves , dampners, one way valves (PCV), check valves, etc.
Less likely would be electrical source (spark to ground relays etc.).
The fact it appears to reoccur right after oil and filter replacement, points to the oil filter by pass return valve making the noise.
I also thought what part is located on the drivers side that is not located on the passenger side?
The filter internal bypass valve can have intermittent flutter if the pressure drop at the exit of filter is very close to 8-psi required to operate the fixed spring.
I would try an FL-820S filter which has the bypass valve set 16-psi to see if it makes a difference.
The dynamics that would cause this bypass valve flutter due to intermittent oil pressure/oil pressure drop right after an oil change is hard to determine for anyone but the designer of the coyote oil system.
Here is my stab at it; all modern cars designed for 0-20 or 5-20 oil have reduced capacity oil systems intended to recoup the loss in power and economy expended in driving the oil pump. In order to allow sufficient pressure to float the main bearings with a down sized pump utmost design care and assembly quality is required to assure all down stream oiling locations keep very tight tolerances, that is the only way to maintain pressure at the main bearings with an undersized oil pump.
If the clearances are too high or some oil passage plugs (or restrictors) are missing it could cause a pressure drop downstream of the filter sufficient to activate the bypass valve.
Fresh oil flows better than used oil containing a slurry of particulates thus creating a higher pressure drop across filter after an oil change, this combined with the possible increased leak down of oil system (as discussed above) could cause the bypass to activate with new oil when it did not with used oil.
The only other fluid noise I can think of is cavitation such as if the oil pump pick up is sitting in sludge or other obstruction (like silicone gasket material), with a set oil pump intake restriction cavitation would occur at higher flow rates (such as after oil change) due to the resulting increase in pressure drop at restricted intake side of oil pump.
Cavitation noise in an oil pump is very audible.
P.S. I hope Ford is not stumped by this noise source, and find a lasting remedy