From what I have been able to find out is the resistance is 0-90 ohms with 0 = empty and 90 = full.
What I am thinking (which is dangerous) there is a voltage drop in the 12volt supply feeding the lamps and the fuel gauge. This causes the Gen light to come on and cause the brake light to dim. The Gen light is finding a ground thru the brake light ground when it is on I think.
Why I am focused on the Fuel gauge and Sender unit is that it is not easily removed for inspection. I can take the connector off in the trunk to test (no done yet). That leaves the Fuel Gauge; I now have a spare to use to test that theory.
I know I am on the right track I just need a kitchen pass to work the issue.