A TRACON Controller reported a BE55 had an engine failure and diverted to land at a nearby airport.

Narrative

Come in to open data and the radar controller has 8 or 9 aircraft with a developmental doing on the job familiarization (OJF) for the radar positions. 2 people are in the Tower already before opening data. I immediately notice that the amendment that the radar controller made resulted in a preferential routing that he did not catch. I fixed that and worked data for an hour or so.The traffic continued to build as is to be expected on a summer day and the supervisor called up to combine the controller in charge (CIC) to local; I had to slide to east radar with no break and; the developmental had to get data. I made a comment as to why this new practice of opening extra positions in the Tower is a terrible practice. Our SOP actually references the unpredictable nature of our radar room as to why the data should not be combined to the desk for extended periods of time. Management has 'mitigated' this by leaving it combined to the radar which is exponentially worse. On nice days the VFR call ups make us busy and; on marginal days without convective weather such as this one we get IFR training flights.A few minutes in to taking the east/south positions Aircraft X that was at 8;000 going to ZZZ1 [requested priority handling]. I asked him for fuel/souls/nature of [problem] and intentions. He responded that he lost his right engine and wanted the longest runway that could handle him nearby. I offered him ZZZ2 as it was closest but; the departure from that airport stated the bases at 1;000 and he did not want an approach. He asked for an airport with better VFR weather and; I took him to ZZZ as it was 1;400; the next closest paved runway and; in a low and flat area without obstructions between him and the airport. I gave him the runway dimensions; weather; field and touchdown elevations. I vectored him to about a 2-3 mile final and down to 1;000 MSL where he reported the field in site and; had another aircraft make the announcement on CTAF as he did not want to make a frequency change. Once they were on the ground they evacuated the aircraft so I was unable to establish whether they made it safely to the ground so the training aircraft that offered to make the radio calls on CTAF agreed to do an approach to the airport with a low approach to see if they were safe on the ground. Before he got there the pilot of Aircraft X called to inform us that they were safe on the ground.This is a prime example of why we are going the wrong direction with sending an extra body to the Tower instead of having help available when the unexpected happens. I certainly went to at least almost 2 hours on position during a high stress situation solely to appease a graph made up to appease people that think we are glorified cubicle workers; when in reality we need to be treated as first responders.Suggestion: Resource management.If we want an extra body in the Tower at all times we must not do it at the expense of the ability to meet the needs of the radar that we know is busier; more complex and; unpredictable.