Flight instructor on training flight with student in a PA23 aircraft reported engine failure in cruise. Flight instructor diverted and landed without incident.

The flight initially departed from ZZZ, on an IFR flight plan. Onboard the aircraft were four passengers, one student training for Commercial Pilot Airplane Multi-Engine Land (CAMEL) certification, and myself instructing the CAMEL student. The purpose of the flight was to return all persons to ZZZ1, with the additional purpose of the CAMEL student to receive additional training on flight operations to build confidence and flight time. En route and over the ZZZ VOR, we began switching from the auxiliary fuel tanks to the main fuel tanks. The left tanks were switched first with no issue. The right tanks were switched several minutes later. During this switch, the right fuel selector required greater force than typical. Approximately one minute after the switch to the right main tank the right engine began to fail. I performed the Engine Failure checklist and the Engine Restart checklist shortly after, which resulted in a successful restart of the right engine. During this time, [priority handling requested] with Approach , and assistance in navigation to the nearest field was requested. The rest of the flight was conducted without incident. We landed in ZZZ2 and called a number provided by Approach to let them know we were down and safe. A previous incident at ZZZ3 predeceased this incident. A CAMEL flight assessment (check-ride) was being conducted, and the engine was shut down by the Designated Pilot Examiner (DPE). Both pilots could not restart the engine, and [priority handling requested]. They returned to ZZZ3. The airplane's engines were runup and the flight school's mechanic and owner were consulted. No issues were found or could be perceived as the later flights would not deliberately shut down the engine. A risk assessment on the likelihood and severity of engine failure determined that failure was remote but would be critical if it occurred. This was evaluated to marginal risk, which was determined to be acceptable by the instructor and CAMEL student. In reflection, continuing to position the fuel selector after encountering increased resistance was abnormal and may have contributed to the engine failure. A review of the PA23's fuel system with another Multi- Engine Flight Instructor is planned and will be logged.