^X2 The Jeep can act real strange if the battery is about to fail or terminals are not clean & tight.
I like to check occasionally the AM volts reading before starting, as well as after starting, the output charging voltage.
Distilled water can be added if you have removable caps, if it's low, & a trickle charge overnight, is recommended before a load test.
Cold weather ***** the cranking amp/juice from a battery as well so, a load test will advise you if a replacement is required.
Start with that and if all is well,the battery's good, yet even then the dash lights still come on, then it's onto codes or connections.