I can set the date & time and sunrise and sunset; however, the instructions to program are obscure to me. I want it to come on at dusk and go off at a set time.

1) Question posted under ST01C
Open following link for ST01C instructions with programming illustrations, plus wiring illustrations and battery information.
http://waterheatertimer.org/ST01C-program.html

2) The ST01C cannot be set for on-at-dusk and off-at-programmed-time.

3) If you have different timer than shown above, then add a comment with description of timer buttons for possible identification.

4) I have not tested the following timer, and it may be same as all other in-wall timers, but it is possible that the new GE 15312 sun-smart timer can be set for on-at-dusk and off-at-programmed-time. BUT I am only reading the instruction manual for a new product, before people write the company and then the manual gets changed.
Wiring for this timer is more complicated that ST01C
http://waterheatertimer.org/pdf/GE-15312-sun-smart-Manual.pdf
http://waterheatertimer.org/GE-timers-and-manuals.html#15312

5) There are numerous outdoor plug-in type timers that offer on-at-dusk, and then off 2 4 6 8 hours later.
http://waterheatertimer.org/Woods-timers-and-manuals.html#2001

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