check EPAS connections
These cars have Electronic Power Assist steering. I'm no expert on EPAS but when I did my first oil change on my 2014 GT I noticed that the connections for the EPAS were right at the bottom of the steering rack. In fact I noticed a little corrosion on the connection even though it was somewhat protected from road grime by the plastic shield. You may have a loose or corroded connection here. It could be making and breaking the connection intermitanty and be a little worse on wet roads. It's worth a look.
2014 GT premium convertible - ruby red