Oh boy, the plot thickens!!!
I went to Lowes, picked up the longest (3") screws that would fit though the mounting holes in the wall bracket and started to re-check position before drilling.
Well, the stud finder confirmed the markings on the wall and I decided to drill a small pilot hole to start. Starting where the top left mountng screw would go, I drilled into the sheet rock, but felt no stud behind it!?!
I took a finishing nail that was longer than the drill bit and slipped that into the pilot hole and still no stud!?!
I then took a 10" length of straight wire coat hanger and fed that though the hole. Finally, I hit the stud. When I measured the depth of it, it was 4 1/4" deep!
I'm guessing that since this front wall of my room used to be the rear outside wall of my house (before we built the extension) the stud finder was actually reading the old (original) stud, not the outermost studs that framed the room when it was built!!!
At this point, I tried the good old fashioned stud finder method and rapped my knuckle across the wall and listened. It confirmed what I already knew with my pilot hole - no stud in that spot!
From what I can tell now, the outer new room build studs that actually back themselves up to the sheetrock in that vicinity of the room are 24" apart.
So I am at a standstill right now.