So, the Fuel pump finally reared its head as a problem. The tank was dropped and cleaned, pump replaced, lines blown. They also replace any part in the EVAP that was still under warranty. I couldn't believe how much smoother and quieter the H2 ran when I picked it up.
Then I took it to fill up - ugh. It didn't want to fill. The pump would shut off at every $2.00. back to the shop. Tank re-dropped this time they put more effort into blowing the lines and found some lines were still clogged. They probed and blew; they check the other EVAP lines and blew. Got the H2 back, no problems filling, no "Tighten Fuel Cap" dash warning.

Success, for about 1 week.
Then back to the original problem - "Tighten Fuel Cap" dash light and alarm warning. This time it came on in about a minute as opposed to the original 4 minutes.
I did notice that the H2 seemed to run a little rough as compared to the prior days
The only thing I can think of is that those 1-way valves on the tank must be clogged.

Question does anyone know what sensor triggers the "Tighten Fuel Cap" dash light and alarm warning?
Is there some way to redesign or disconnect this EVAP system that will still allow the tank to vent properly?
I'm going to add this to the original Post.

 

A MIL (warning light) normally has an associated DTC, this is "key" diagnostic info so it's worth retrieving this code, if you already have it please post.
There are many EVAP related codes:-
P0442, P0443, P0446, P0445, P0449, P0451, P0452, P0453, P0455, P0461, P0462, P0463, P0464, P0496


P0445 is a "Large Leak Test" failure, it could be this one but the manual is unclear on which codes are associated with the "Tighten Fuel Cap" message.

The attached pdf contains some useful info.

AI gave this response:-

Understanding the "Tighten Fuel Cap" Message

The "Tighten Fuel Cap" message in a Hummer H2 typically indicates a potential issue with the vehicle's evaporative emissions (EVAP) system. This warning can appear even when there are no diagnostic trouble codes (DTCs) present.

Common Causes

• Loose or Damaged Gas Cap: The most straightforward reason for this message is a loose or damaged gas cap. Ensure the cap is tightened properly and inspect for any wear.
  
• EVAP System Issues: Problems within the EVAP system, such as clogged lines or malfunctioning valves, can trigger this alert. The system is sensitive to pressure changes, and any leaks can cause the warning to appear.
  
• Filler Neck Problems: Issues with the filler neck, such as rust or obstructions, can also lead to this message. Cleaning or replacing the filler neck may resolve the issue.
  

Diagnostic Steps

1. Check for Codes: Even if the message appears, perform a thorough scan for any hidden DTCs. Sometimes, codes may not be immediately visible.
   
2. Inspect the Gas Cap: Ensure it is sealing properly. A damaged cap can lead to pressure loss in the EVAP system.
   
3. Examine EVAP Components: Inspect the purge valve, vent valve, and associated hoses for blockages or damage.
   
4. Pressure Testing: Conduct a pressure test on the EVAP system to identify any leaks.
   

Conclusion

If the "Tighten Fuel Cap" message persists after checking these components, further investigation into the EVAP system may be necessary. It may be beneficial to consult a professional technician for a detailed diagnosis.