Signal mirrors can be used without a definite target — the strategy of painting the horizon
if "no ships or aircraft are in sight" has long been advocated [1].

I've done so myself (in training) when I wasn't sure where along a ridge (or range) the Boy Scout team was[1].

In most of the 20+ recent signal mirror rescue news reports, the survivor's flashes were spotted by a rescue plane or helicopter.

I would expect most such cases to be deliberately targeted flashes —
rescue aircraft are noisy and easily spotted at long range against the sky. Ground search parties are far stealthier.

Only one recent case seems a good candidate for "painting an area" rather than "painting a target":

• Hunter stuck on Thunder Mountain Cliff (hiker's distress flashes spotted at school - two dimensional search?)

In sixteen of these recent signal mirror rescues the signals were to helicopters or planes.

While some of those may be (as in your Davis-Montham example), at least initially area search rather than targeted,
I would expect most were targeted, and some clearly were - the most definitive being the 2008 Patrick Higgins Case :

"Higgens helped tremendously in his rescue as he was unusually knowledgeable in the use of the mirror as he tracked the plane with it."

So, from this unscientfically chosen sample of signal mirror successes, I'd say most of them were cases of signaling to a definite target, usually a helicopter or plane.

This suggests to me that, while linear and area search have value, most signal mirror rescues seem to be the result of aimed point-target signaling.

[1] Recognition of linear or area signaling vs. point target:

• the 4th instruction on the back of the current US military mirror, the glass retroreflective MIL-M-18371E mirror, is:
  "EVEN THOUGH NO AIRCRAFT OR SHIPS ARE IN SIGHT, CONTINUE SWEEPING THE HORIZON FOR MIRRORS MAY BE SEEN FOR MANY MILES, EVEN IN HAZY WEATHER."
  
  
  
  
• The very first purpose-built precision aim US military signal mirror,
  the double-sided aimer"cross-in-glass" GE ESM/I of 1943 had as the last line of the instructions:
  
  "Practice sweeping horizon with aimed beam even if no rescuer is in sight, as mirror has range of up to 10 miles".
  
• 
  From the 1905 Manual of Visual SIgnaling of the US Signal Corps, p.80, last paragraph:
  
  "To find a distant station, its position being unknown, reverse the catch holding the station mirror and with the hand turn the mirror very slowly and full azimuth distance in which the distant station may possibly lie. This should be repeated not less than twice, after which, within a reasonable time, there being no response, teh mirror will be directed upon a point nearer to the home station and the same process repeated."