Atwood 6 gal gas/electric hot water heater seems to have a short. When breaker in travel trailer for the water heater is switched on, it immediately trips the GFI in my garage circuit.

Copy following link for general TP troubleshoot walk-thru
http://waterheatertimer.org/How-to-replace-TP-valve.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

I do not have specific answer.

Open following links to identify product, download service guide and download manual for the different model numbers, plus parts list and other resources:

Page 3-4 of following manual shows switch settings for LP gas.
On-line manual can be word-searched for 'switch.'
This water heater has remote switch, which is the switch you are talking about. It also has limit switch and ECO (energy cut-off switch)
http://waterheatertimer.org/pdf/Atwood-installation-maintenance.pdf

http://waterheatertimer.org/pdf/Atwood-Water-Heater-Service-manual.pdf
http://waterheatertimer.org/Atwood-water-heater-resources.html

I'm thinking when you say black box, that you also have a wall switch with a symbol like a lightning bolt and you switch that on as well as checked breaker panel to make sure breaker is on as well.
With that said, you'll have 2 of 3/8" nuts holding that black cover on. Remove top one and loosen bottom one and pull cover off. ( Be sure power is off to unit while doing this.) You'll find the element in behind it. Put a voltmeter on black to element (red probe or alligator clip) and (black probe) to ground where you see green wire connected to tank. Turn breaker on then switch at wall. You should hear a relay click and 120 Volts should show at black wire ( red probe) . If you've got 120 volts there, shut off all power, drain water heater and replace element.

Sounds like you have a short in wiring for 120VAC system of water heater. Shut breaker at panel off, and remove cover on back of water heater to look for any burnt wiring at connections such as switch, or thermostat/eco assembly.

Yes. As long as it's an atwood 6 gal., the opening should be same dimensions. Keep in mind that you will need to supply hydro to water heater in order to operate it on electric, as well as switch etc. For electronic ignition of gas, you will need to supply a 12 VDC source, and switch as well.

There should be an internal reset button.

The two switches control the water heater either in the gas or electric mode. The switch with the lights would be for the gas operation, and the switch without lights would be for the electric mode. Prior to operating either switch, make sure the water tank is full of water. Turn your hot water tap on, if water comes out, tank is full. Connect trailer to 110 Volt source, turn circuit breakers on, Place switch without lights to on position. If water does not heat in 45 minutes, Install new heat proble. The gas mode should be repaired by someone that is familiar with that system. Atwood can provide you with a local service center.

Re: electric setting. Are you sure all switches are on, breaker in panel, any wall switches, plus switch usually at back of water heater where hydro connects as well. If yes, you may have to remove cover where power cable at back is connected (shut off breaker and any switches, and test to be sure power /hydro is off to water heater before removing cover) Are you experienced in this area? If not, it may be smart to get a technician or electrician to test for power from there.There should also be a reset as well in there on thermostat. Thermostat and ECO can be tested as well for continuity while cover off.

As far as gas not shutting off on gas, thermostat and ECO should be tested for proper operation as well as proper positioning.They should be up against the tank in order to work properly,

You will be happier if you replace it
Repairs seldom last very long with this type of problem

sell it and buy beer? Sorry, I know its not a good answer but you asked ANY thoughts.