Join Date: Jul 2013
Location: Orange County, VA
Replace the gas cap. They're cheap. Just because it goes on fine doesn't mean it is holding the pressure required by the fuel system. As for the TPMS light, There is no sensor in the spare. At least not on mine. I have a 2014 with a full size spare. I changed the spare to match the tires I am running currently and have changed it out once before. No TPMS sensor in the wheel. Either check in inflate the tires properly and if that doesn't make it go out, then have a tire shop diagnose and tell you which sensor is not reading. They use lithium watch batteries and do go bad. They can also be found for pretty cheap and having a bad unit replaced shouldn't cost more than 50-60 bucks all done.
Ignoring these messages can only lead to other issues farther down the line. Take care of them now while they are still cheap, easy fixes.
2014 Black Jeep Patriot, Latitude, FDII, Sun and Sound package, remote start
2015 White Jeep Grand Cherokee, Limited, Luxury group II