How to troubleshoot outdoor lamp/electric functionality?
I'm just sharing the answer and outcomes to this question. Hope it helps someone else. Thanks to everyone for the comments especially isherwood and  Ed Beal for leading me in the right direction.

I found additional GFCI switches and outlets in the backyard shed. The original owner apparently wired this in series to the outdoor lamp. 

There was a GFCI outlet with a reset button which when reset did not actually reset (the light on the reset tab stayed open):



After that, I found an electrician and pointed them to the problematic outlet. Another hint was that the outdoor light outside the shed had been displaying unusual behavior (it has a motion detector and it started to stay on all night at about the same time our lamp went out.)

Outcomes:

Once the shed condition was repaired, the lamp and electric socket began working again. I sure would like to really understand what the technical fix was (if anyone is inclined to share some insight; it'd be much appreciated). I try to learn from each experience so I'd like to understand what could have caused this and how it was fixed.

I guessed that the original issue might be related to weather and added a flip box over the two outdoor switches. 



Just not sure how the electrician resolved the open circuit in the shed.