I have a 2013 Madone with the same issue, I know it's the headset bearings because eventually rust started coming out of the gap between the fork and the headtube, and if left overnight after a damp ride the bars won't rotate at all unless you give them some force and get the bearings moving again. It now presents itself as a clicking just like you describe.

Unfortunately for me, the Madone has integrated angular contact 1 1/2" to 1 1/8" cartridge bearings. I've dropped the fork and greased everything so that the bike can still steer, but the upper and lower cartridges are basically shot and need to be replaced.

I emailed Trek for exact measurements on these bearings after buying a set I thought would fit with no luck. They told me it's impossible to know the exact measure without having the bike seen by an authorized dealer, and they need a special tool to remove the bearing race on the fork crown.

That's confusing for me because it looks like they're just 2 cartridges that sit in molded grooves, and I gave them my model, year, size, fit type, and serial # so you'd think they would be able to give me information on replacement bearings. Oh well, guess I'll end up swallowing my pride and having a shop do it for what will probably be $100+ on a job that shouldn't cost more than $20.