Your Atwood electric/gas WH uses the SAME set of t-stat/ECO for both along with that thermal fuse.
SO gas works..those components are good
Same goes for that 2A fuse on circuit board
Electric element is located on backside of WH Tank under protective cover
The 120V AC to element is 'triggered' by a DC Relay---also under that protective cover
12V DC power goes to both electric & gas ON/OFF switches and from switches when ON to circuit board.
Electric System
DC to circuit board via the WHITE wire when switch is turned ON
Then thru BROWN wires (Thermal fuse/t-stat) then RED wire to/thru ECO (milivolt signal only)
When that circuit makes up DC goes to Relay to trigger 120V AC via YELLOW wire
DC Relay makes up..120V AC goes to element via BLACK wire...thru element and then back to AC Panel via WHITE wire
Turn Electric switch ON
Check/Verify 12V DC on WHITE wire
Check/verify 12V DC on BROWN wires
Check/Verify 12V DC on YELLOW wire
(RED wire to ECO/gas valve must have milivolt signal or YELLOW will not have DC Voltage)
Got DC Voltage.......
With Electric Switch ON
Check for 120V AC across the element terminals (Black to White)
No 120V AC then check for tripped AC Circuit Breaker/bad wiring
Got 120V AC across terminals
Turn Electric switch OFF!!!
Check for continuity....
Between the element 2 terminals (Black to White)....should have continuity.
IF NO continuity---element is bad
Between White wire (common) terminal and flange of element
Should NOT be any continuity.....otherwise element is shorted
Verify Ground (Green) wire has good clean/tight connection
Element is a 1400W Screw in type.....takes a 1 1/2" 6 point socket
Atwood 2004 and newer electric/gas wiring