A BE60 pilot reported right engine failure and diversion to nearby airport.

Narrative

I conducted a flight from ZZZ to ZZZ1 for pleasure. I chose to descend from 5500 feet to 3000 feet to intercept the RNAV XX for practice approach in visual conditions. I continued to ZZZZZ for the approach. After turning inbound at ZZZZZ1; the right engine ran rough and quit. I identified; verified and feathered the Right engine; [requested priority handling] with ZZZ and asked for vectors to ZZZ2. They recommended the nearest ZZZ1 or ZZZ3. They gave me ZZZ3 frequency and I called; [requested priority handling] and asked for runway XX. I continued flight; landed without incident and had the airplane towed to parking at ZZZ3. I did an initial inspection and called my mechanic. We discussed mechanical fuel pump failure as a likely possibility. I had the airplane fueled for a possible flight back to ZZZ. I opened the cowl doors and with a flashlight inspected the engine compartment on both sides of the right engine. Everything looked fine. I did a preliminary restart using only the electric auxiliary fuel pump and the right engine ran fine. I contacted a second mechanic about flying with only an electric fuel pump on the right side; and we discussed the possibility of not having enough power for flight. I did a thorough preflight; started both the left and the right engines; and got a taxi clearance for a high speed taxi on runway XY for a power check. I explained my intent to taxi back for VFR departure to ZZZ if the power check was good. The Engines showed full take-off-power on the high speed taxi with no discernible difference; Manifold Pressure or RPM; left versus right engine. Both had full take off power; with normal fuel flow.I taxied back to runway XY; got a VFR clearance and departed for ZZZ without any problems.Once on the ground at ZZZ; I again checked the Mechanical Fuel pump by turning off the electric fuel pump; and the right engine again failed.A replacement mechanical fuel pump will be installed next week.