[kaptain]

Thank you very much, Richard, for taking the time to read my issue and write answers for me and for your compliment!

Here is my preliminary update:

I started tracing wires today and made corrections to Xentrex Echo Charge the wire, just like you described.
However, Echo Charge still BLINKs green, and the chassis battery still doesn't get charged.
The test is done with the chassis battery measured at 12.8v, and the house battery at 14V (charging). The two Disconnect Switches are both ON (INVERTER and CHASSIS BATTERY).

So I decided to remove the Xentrex Echo Charge off from the coach and test it on a standard-alone adjustable DC power supplier and a single used car battery, which is measured 12.4V. Echo Charger blinks green when its input is initially set at 13.0V, no output, thus not charging.
Then I started to turn the knob on the DC power supply to increase the voltage. Not until the Echo Charge input voltage reaches 16.8V it start producing output, and LED turns from BLINKING to SOLID.
The voltage reading across the 12V car battery is now increasing, indicating charging is in progress.

Then I start the counter-turn the knob to reduce the voltage on the Echo Charge input side. It starts to BLINK green when its input is below 16.3V.

I looked at Echo Charger to see if there was anything burned or otherwise abnormal. Nothing appears wrong except it looks dusty and dirty.
So I used pressure air to clean it. Re-test, this time it seems the Echo Charge can produce an output when the input is 16.4V, seemingly a slight improvement.

I decided to give it a thorough cleaning. I opened the Echo Charge enclosure, whipped it with alcohol, blew it to dry, and re-test. The result is almost the same as the first test, no improvement. So the dust wasn't the issue.

I am now waiting for a new Echo Charge and will provide a further update next few days.
Thanks, Richard, and all who spent time and shared your insights and knowledge.