If you wand to do search and rescue consider joining CAP (Civil Air Patrol), or a similar aviation based SAR organization. CAP does all SAR/DR work from their corporate aircraft. Nationwide CAP has over 550 aircraft distributed across the 50 states and Puerto Rico. CAP requires pilots who fly SAR/DR to be current, have annual check rides with CAP 'Stand Eval' pilots, acquire and maintain SAR/DR "Mission Pilot" skills, and successfully pass a biannual 'Mission Pilot" checkride. In Washington there's an officially recognized organization called "WSAR" (Washington Search and Rescue). WSAR pilots all provide their own aircraft and the State pays for fuel. In both cases SAR/DR aircraft do not launch without oversight and coordination.
Generally it's a really bad idea for someone to fly into the middle of a SAR, DR, or similar operation. Midairs, interference with official SAR/DR missions, potential harm for persons on the ground where conflicts occur between the organized searches and those who roll their own, etc. etc. etc. all argue strongly against a just DO IT' approach to SAR/DR. There are also some fairly high personal risks for pilots to consider if untrained or unfamiliar with SAR/DR flying. About 2004 a friend of mine took a local deputy up to search for a missing person... He had a good relationship with the local Sheriff and had helped out in the past with good result. Unfortunately my friend forgot who was responsible for looking for the missing person and who was responsible for flying the airplane. Both men had very nice, but very unnecessary funerals.
Here's another, different example that happened to me four years ago. I flew the person who managed a busy show over a vigorously burning wildfire near the Washington/Idaho line. My job was "fly the airplane" and "See and Avoid". Things were getting very busy when I spotted a Supercub as it flew into the fire traffic area below us and from the north. The aircraft flew directly over the middle of the fire about the time a CL215 started his first water drop run. Another CL215 and a couple of helicopters were also in the airspace (plus us). Fortunately for all the citizen pilot was on 122.9, the frequency for a nearby airport. The pilot heard my broadcast in the blind that there were multiple aircraft working the incident, and complied with my request (order, actually) that the aircraft immediately depart the airspace. Regardless, the first CL215 aborted his drop which cost a few hundred dollars of airtime, and returned to orbit (costing a few hundred more) until the airspace was clear. Meanwhile the second CL215 remained unnecessarily parked in his orbit around the fire waiting for the first CL215 to complete his drop (Ca-ching Ca-ching for another thousand $$ or two). The pilot of the Supercub was clueless that five aircraft were working this fire, or that his/her careless entry forced a pause in suppression activities. Fortunately, in that incident the outcome was just a few hundred trees that torched unnecessarily, a few more acres were burned over, and a few thousand dollars wasted.