Hi there,
Interesting that you put my name in the head lines. Guess you wanted my attention! Thanks, I think?

I don't know how helpful putting in the new wire was but it should have eliminated the harness as an issue.
There is an electronic temperature compensation board built in to the instrument cluster that goes haywire.
This causes erratic temperature response on the gage. It stages the heating current to the gage so it only moves to one certain spot until there is a large enough discrepancy to warrant a change instead of seeing a gradual change like a analog system. It didn't or doesn't work reliably after a few or many years of service. In other words for the most part, it was a bad idea!
The best thing to do with it is go inside the cluster and see if it has been removed. If not remove and add a jumper wire. Place it onto pins, one and three, to bypass any more of its monkey business with it.
More information is at WWW.cleanflametrap.com.

The dash temperature gauge will not move up if the engine is cold. Might explain why you did not get a reading on one of your tests after you changed out the sensor and wire.

The gage will only reach up into the lowest area of the curved band at 120 degrees.
With a 180 degrees thermostat will be just below horizontal at about 8 to 8:30. It is better to run a 192 thermostat for slightly better fuel economy and emissions. This puts it at 9:00 or about the width of the needle +\-. I prefer the Wahler brand due to being made of brass and are dated to when they were manufactured. Most last upwards to 17 years in my cars and repeat their response at their setting.

You mentioned a ECT computer ECU sensor change out which is only good if the engine was running poorly. I don't think you needed to do that as it does not effect the cluster gauge.

Now, I think we have discussed all that can be talked about with the temperature gauge.
The rest you wrote about is more about power supply from the battery.
The battery itself might be the main issue here.

If you have to to keep repeatedly putting it on charge, after such short moments of usage, it's a bad battery.
A bad battery can be put on a charger and it can and will fool the charger. Some chargers have green lights that trigger falsely into telling you that it is fully charged or shut down into a maintenance mode.
Bad cells will charge up a superficial voltage within the depleted electrolyte or the plates can be so sulphated beyond reacting with any acid. In other words, the cell or cells cannot contribute amperage capacity through the cells and the loaded down system will fall on its face.
This is when its just a click and lights go out.

RStarky posted the next issue that controls letting power out of a good battery. Cables!
There two ways power gets out of the battery and into the cars various loads.
One is the tiny wire off the positive post that feeds a junction box on the fender. This then feeds the fuse panel in the drivers door hinge area. You got to have good connection along this route.
This feeds the ignition switch and the instrument panel.
If the voltage drops below nine volts most lights will be very dim or go out. Having corrosion or a weak battery brings on this response very quickly.

The ignition switch controls several functions along with purposely turning of some accessories.
The ignition switch hooks the starter solenoid to the battery.
The solenoid switch itself takes quite a bit current to operate it. So much in fact that this is why the accessories get shut off in position three. The blower fan goes off because it draws half of what a fuse on the wire to the fender carries.

Now from my experience, I know the solenoid can have internal issues of just clicking but not engaging the starter motor. The contact plates inside it just barely does not make up contact. It can be fixed or replaced but it has to be removed.
You very well can have a problem right inside the solenoid and a low battery helps promote making the solenoids fail.
If the cables are in good condition on a good battery the "second way power gets out" into the cars starter system has to be through that solenoid Switch!

Now there is a wire, located up beside that gray connector, that can bypass the whole previous system to roll over the starter motor. This wire will have a flat female spade terminal that can be jumpered to the cars battery positive post.
This will click the solenoid to close and turn over the engine. You can rapidly test that solenoid until it engages the starter motor or call it dead!
You will want to verify that the car is in neutral or park before testing the starters function.

Test again with a known good battery and cables you might get a surprise after taking a step by step approach.

Phil