My jeep battery keeps getting killed. We have tested the alternator and battery and they are both good. The left turn signal and some other lights also don't work majority of the time. What could this problem be?
Need a lot more information to go on. How long does the battery take to be drained? A day? A month? How old is it? Measure the battery voltage with the engine off and with it running. Those numbers will tell us how to proceed.
Did you check the charging system on the vehicle? Does the battery have a full charge at the moment? You can't do any testing unless the battery has a full charge. Use a digital multi meter across battery posts, everything off, the generic spec for a full charge is around 12.6 volts. Start the vehicle, take second reading across battery posts, if the charging system is working, the second reading should be higher than the first.
Any applicable trouble codes? You could have too much battery drain with everything off, check amp draw. If amp draw is too much, you pull replace fuses, one at a time, when you pull the fuse on the problem circuit, the excess drain goes away. Check the vehicle in the dark, make sure no lights are staying on, interior--under the hood--glove box, everywhere.