I cannot make precise sense of your question.
However I agree, the manual for GE 17117 is not clear.
1) A number of folks are writing in about this particular timer, with same MODE problem as you.
Some folks, the timer skips over auto.
Some folks the timer just doesn't come on.
Facts are facts, some timers are busted on arrival.
But let's look at the problem from three different directions and see if it helps:
2) Steps from manual:
When you finish programming, press clock button to return to current time.
Next set MODE.
Press MODE button and timer enters override ON-OFF. Override reverses whatever program is operating at that moment.
Press MODE button again and timer enters RDM random mode, and lights turn on-off randomly.
Press MODE button again and timer enters AUTO >>> auto is correct setting that lets programs run.
Here's the trick: after setting MODE to auto, press clock button again and current time displays.
If timer will not perform these steps, then timer is suspect
If timer performs these steps, but programs won't work, the timer is suspect or programming is suspect.
3) Check programming for conflicts and overlaps that cause timer not to function 'as expected.'
Some timers skip over conflicting programs, some timers simply stay on, others stay off.http://waterheatertimer.org/pdf/GE-15117-Manual.pdf
Example of conflict is event1 ON at 7am TU > but event1 OFF at 11pm All-days. Both event1 ON and OFF events must have consistent days >>> so change TU to All-days.
Another example is event1 ON 7am OFF 11pm TU >> but event2 says opposite, or has overlapping times.
I suggest folks make a schedule of programs before starting.
To review and change programs, start with current time showing in display: Press PROG button and scroll through event1 ON, event1 OFF, event2 ON, event2 OFF, etc.
Write down the events and make a chart.
Look for overlaps, and check for days of operation, and make sure each event ON has corresponding event OFF
4) If events are correct, and timer MODE button functions, but timer still doesn't work, the final suspect before calling the timer busted, is circuit problem. Use circuit analyzer on receptacle. Or plug timer into receptacle on different breaker and see if problem persists.