We know that Luke Skywalker vanished after
Kylo Ren killed his students.
But, for some reason, there’s a map to his location. That seems odd for someone who doesn’t want to be found, at least not by the wrong people.
Throughout the movie people kept calling it a "map to Luke Skywalker" but I think they were being a bit sloppy with their phrasing.
At one point, Han mentions that everyone believes Luke left to find
the first Jedi temple.
The map everyone is looking for, then, isn't a map to Luke. It's a map to the thing Luke was looking for. This is significant, because two different characters have most of the map already:
Kylo Ren tells Rey this, and R2-D2 displays it at the end.
Both characters got this map information from the Empire's records, so clearly the map predates Luke's journey by a long time. In fact, in the novelization, one of the Resistance members makes this same connection, after being told that the Imperial Records had the rest of the map:
'Admiral Statura nodded in agreement. “It makes sense. The Empire would have been looking for the first Jedi temples.'
What's missing from this map -- likely, missing from the Empire records -- is the last piece. However the Empire got this map, one section of it was lost/damaged/never scouted/etc. That is the thing that was found at the start of the movie and that everyone else needs to find Luke.
Consequences: If my cached Force user arrives at my location shortly after the major Force ripple, it will be time to set out to shut down the Dark. Otherwise, continue hiding.
This answer may be colored by the pre-Disney writings about Palpatine's Xanatos Gambit regarding defending the Galaxy against the Yuuzhan Vong.
I think you answered your own question. He doesn’t want to be found by the wrong people, so he created a two-level authentication challenge that presumably, only the right person/people/Wookiee can complete. Finding the fragment is the first part, but anyone can do that. The second part is to get R2-D2’s approval. Those requirements are never made clear, but the implication is that R2-D2 must validate that the right person and/or Wookiee found the fragment. You can infer that Rey is the right person, as R2-D2 failed to activate until she presented herself.