First off welcome to the forum. Just a suggestion, take some time and read through the threads in the [Please login or register to view this link] section of the forum. Sometimes simply going back to basics solves the problem.
Using the mag mount until you get things going shouldn't be a problem. If it's a 2:1 match the radio will be fine especially if you keep your key ups (transmissions) short. That being said and focusing on your rear mount, the first thing to check is the feed line. A simple continuity check should yield whether it's okay or not. On the PL-259 connector in the back of the radio, measure between the center pin (lead) and coupling nut (shield). There should be no conductivity between the two. If there is, then go to the stud assembly and disconnect the connector(s). Check it from that end. If it shows good, then move on to the stud assembly. There are two basic type stud assemblies that use different coaxial connectors. If yours has the SO-239 (receives the PL-259 UHF connector like what goes in the radio) then there should be no insulator on the bottom of the mount and stud, just the top to insulate the antenna from ground. If you have the crimp on ring connector type (my personal favorite) then the stud should have an insulator on both top and bottom to keep the antenna from shorting to ground. Assuming your clear on that, take a measurement from the base of the antenna/top of the stud to the mount. There should be no continuity between the two. If there is any, there is likely part of the problem. Replace the stud assembly and/or insulators as needed.
A couple things about the mounting location, and overall installation. I too have a couple of Jeeps ('02 TJ & '95 XJ), and usually the reason guys mount them on the back like you did is for looks. That's fine, but it really does limit antennas you can use effectively and sets you up for side reflection which may be impossible to overcome with the antenna you have. Not seeing the entire installation I'm merely speculating on what I've seen other XJ, ZJ, and WJ owners do. Almost all of them end up having some trouble mounting there....usually counterpoise (aka 'ground') connection. Shiney metal is your friend, and making sure you have that isn't likely to be measurable with a meter. I personally like adding at least one self tapping screw(s) through the mount into the sheet metal. That's what's always worked for me. And you'd be wise to consider investing in an inexpensive SWR meter like the Radio Shack one for $45. It's a good value and allot of people own them. I have one in my pick up truck, but more to see what my amplifier(s) are doing more than anything.
Hope that helps a little and good luck.