Before I go into great detail, lets be sure you do not simply have a bad battery. Measure its voltage with a digital voltmeter. You must find 12.6 volts if it is good and fully-charged. If you find it is closer to 12.2 volts, charge it at a slow rate for at least an hour, then test it again. If you find it's around 11 volts, it has a shorted cell and must be replaced. Your observation of unusual light activity is a common clue to a defective battery.
Part of what you are describing is extremely common, but you have some additional observations and clues that I have not looked for in the past. For the moment, lets overlook the lights and focus on the starter motor. The goal is to keep it in the bad state so we can do some tests. It sounds like that will not be a problem.
Use a test light with the ground clip connected to the battery's negative post, then touch the probe to the larger battery cable on the starter. That is the red arrow in my nifty photo. You will see it light up full brightness. Now have a helper turn the ignition switch to "crank". If you have this very common problem, you will hear a single, rather loud clunk from the starter, and the test light will remain bright. That clunk indicates the solenoid is functioning mechanically so there is no need to test that part of the circuit, (orange arrow).
What commonly happens is the contacts inside the solenoid burn and arc away, then they do not make a good connection to send current to the starter motor. If you want to go a step further and verify this, lift the blue rubber cap, (blue arrow), then poke the test light's probe on that connection. You will find 0 volts until your helper turns the ignition switch to "crank". Then, you should find full battery voltage which will be drawn down a little by the starter. When it is working and cranking properly, expect to see a slightly dimmed test light, or, if you're using a digital voltmeter, at least 9.6 volts. When the solenoid contacts are burned away, you will still get that nice solid clunk, but the voltage on this terminal, if any, will be too low to make the test light glow, even a little.
The second photo shows what the solenoid contacts look like. Many hardware stores and farm and home stores have rebuild kits that include all four of these. You use the "battery" contact, which is the same in all of these starters on Chrysler's and Toyota's, and you use the one of the other three that matches your old "solenoid" contact. If you do not want to go through the trouble of doing this repair, the solution is to replace the starter.
The kits also include the plunger with the contact disc. Typically that does not have to be replaced, and there is one clinker to be aware of. The center shaft that does the mechanical part of the job comes in three different lengths. Since all of these starters interchange between many years and models, it is not always possible to know which version of this starter you have until you get it apart. The two plungers used in starters for Chrysler products are different in length by 1/8" and you have a fifty percent chance of buying the right kit. If you are doing this repair on a Toyota, they used a plunger that is very much longer, and you cannot buy that one anywhere except from the dealer. As I mentioned, it's rare that you must replace the plunger as the contact disc on it holds up pretty well, so if you buy the wrong kit, just use the contacts as needed, and reuse your old plunger.
The single most common clue to this problem is it always starts out as an intermittent no-crank problem, and it will crank after cycling the ignition switch a few times. Every day it will take more and more tries before the starter cranks the engine. The last time this happened to my mother's 1995 Grand Caravan, I ignored it for too many months until the day she lost count after 700 tries and a blister on her thumb, but it did eventually start. You can be sure I heard about it that day!
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Sunday, May 27th, 2018 AT 6:59 PM