"When I bought the rig I didn't want it to be a "fixer-upper" but I'm finding out that it's slowly becoming just that."
Well, and don't take this as being a smart ass, you are dealing with a nearly 30 year old mechanical thing! It has had an unknown life before you, and no matter how it looks or what you were told by the seller, it will have parts and systems that go bad.
Owners of older vehicles are typically tinkerer's and shade tree mechanics, and most enjoy this aspect of ownership. If not, it will be a costly relationship to pay others to keep up with repairs.
Buy the factory manuals, read them, ask questions here, and dig in. For the most part, older LandCruisers are simple and Mud can answer and help when you get stuck.
The type of problems you are experiencing are common when 24v vehicles are mixed with 12v accessories - especially alarms, as most alarm installers have never really seen a 24v vehicle before!
Another thing to check is to make sure the ground connections, and there are several, are good - tight, clean, and connected to battery. Many odd problems end up being bad grounds. IMHO, a LC can not have too many grounds! Battery to engine, battery to frame, battery to body, battery to starter, engine to body, body to frame...you get the idea.
Welcome and good luck.
