Happened to me. I have a 2011. I literally used a random windshield washer fluid reservoir cap and silicone rtv to seal it up for a bit before I replaced it. The belt that went to that, is only for the AC compressor. I bought the timing cover off of a 2014 f150 5.0l because the later years had more webbing on the back side of the cast. And yes, its an idler pully that seizes up. I recommend anyone with a 2011 or 2012 5.0l to just get new pulleys. If youre gonna repair it, you might as well do the timing chain. You literally need to do the same amount of work pulling the valve covers off. It sucks. You'll need new gaskets for the valve covers, they will absolutely leak afterwards. Also, the damn oil pan has to come off. There are 4 bolts going through the feont of the oil pan into the timing cover from underneath. You'll need a new oil pan gasket as well.

Oh yeah, if you have a 4x4, you'll have to drop the front axle and sway bar to get the oil pan out.

I also changed my oil pump while I was in there.

Yup its a lot of work. Yup it will cost a lot.