I'm a huge fan of patching tubes with the flatted tire on hand. Now I can match up the patch to the tire and know exactly where to look for the problem.I don't rest easy until I know what caused that flat. If at all possible, I patch tires at the roadside and reuse the tire. Both to locate the issue and flatten the patch with tire pressure against the tire. (And I still have 2 spare tubes to go.)
Now, there are holes so small that finding them outdoors with roadside noise is impossible. The spare goes in and I am nervous 'till I get home unless I found the cause with my eyes or fingers. At home, I inflate the tube and find the hole under water. Then patch the tube, pull the spare and go looking for the cause.
For multiple flats on the same tire, that patched tube tells you a lot. 2 or more holes at your first patch makes the cause obvious. (Or egual distance from the valve on the other side.) A huge help in finding those tiny steel wires from car treads that can be 1/16" long and barely thicker than a hair (and can embed themselves completely inside the tread).