Zombie apocalypse in 3..2…1…. No, wait.
"We cannot win this re-election, we can only elect Donald Trump."
Phew.
The tech to locate handsets is actually in the cellular networks.
You see, for the network to route data/calls to a mobile handset, the network must know where the handset is, respectively in what cell it is located.
A cell is then usually divided again into sectors, with each sector being covered by a so called sector antenna. Most often, a sector covers 60° in the horizontal plane.
The cellular network knows the location of recently active handsets only. But if a handset is has not been active for a while, a special type of short message called "silent ping" may be sent to it. Any handset will reply to that silent ping message, but no indication whatsoever will be given to the end user to inform them about this occurrence. As soon as the handset replies to the silent ping, the cellular network updates its registry with the new location of the handset.
Law Enforcement across the globe uses this technique to create movement profiles of mobile handsets. These profiles are accurate down to the cell/sector level. A cell may be quite small in urban areas (50m diameter), but may be considerably larger in a rural setting (25k or more).
If the cell/sector granularity is not accurate enough for tracking purposes, mobile network operators can offer triangulation through multiple base stations. This can provide very accurate location down to a few meters.
Note that no GPS or other location service needs to run on the handset for this technique to work.