Product review (5 stars): Problem Resolved
My order was received in a timely manner and was a perfect match for the defective timer.  The price was appealing when compared to what my local appliance store was charging for this part.

I electrically diagnosed the problem on my Roper dryer and chased it down to the timer.  I had to do extensive disassembly to my dryer in order to thoroughly diagnose the problem.  If you disregard the time it took to do all of that, the timer itself only took about 10 minutes to replace and confirm proper operation.

My online research on this part leads me to believe it is a frequent failure item.  Maybe I know why.  Days after my dryer was fixed, I decided to disassemble the old defective timer to find the root cause.  I expected to find a burnt or broken contact.  Upon disassembly I discovered there are three plastic cam discs that rotate when you turn the setting dial.  They also rotate as the timer motor runs.  These three cams activate several different switch contacts as the cam lobes rotate.  The problem with my old timer was the retaining tab on the white cam had broken off causing the cam to come out of position.  This explains my troubleshooting difficulty as sometimes switches would activate and other times they would not.  Anyway, with three drops of crazy glue I was able to re-secure the cam.  I've reassembled the timer and saved it for the next time the timer fails.  The first one only lasted about 4 years.  I wish now I had disassembled the old timer and fixed it before ordering a replacement but that's not meant to be a negative reflection on the new replacement part.