Eh? There's no such thing as ETOPS operations with other than two engines.
The ETOPS term also applies to 3 and 4 engine aircraft, although cargo aircraft are exempt from most of the requirements. The FAA rejected the proposed LROPS terminology for 3 and 4 engine aircraft.
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In regard to the OP's question on why tail mounted engines fell out of favor, ETOPS has a lot to do with why three engine designs fell out of favor. Three or more engines were necessary for over water routes back in the day when the loss of an engine (piston or turbine) may have resulted in the aircraft being unable to maintain flight when fully loaded to the closest diversionary airfield.
Several years ago when I noted my flight to HI was on a 737-700 I did some research into the old 90 minute ICAO rule dating from 1976, ETOPS 120 dating from 1985 (along with the 15% extension to ETOPS 138 under adverse weather conditions), ETOPS 180 dating from 1988 (along with the 15% extension to ETOPS 207), and ETOPS beyond 180 which kicked off in 2009 with the A330 receiving an ETOPS 240 certification.
Most North Atlantic routes are flyable under the 120 minute diversion rule, with the 15% extension to 138 minutes. About 95% of the routes on the planet fall under the ETOPS 180 rule with the extension to 207 minutes.
The ideas behind the revised ETOPS rules were that turbine engines are extremely reliable, and powerful enough for a twin engine airliner to maintain flight with a full load on one engine for the required number minutes to a diversion airfield. However, the engines' ancillary systems are potentially less reliable, so ETOPS certification hinges on ancillary system reliability and redundancy built in at certification.
Engine reliability also matters for both the aircraft and for the airline. ETOPS 120 requires an engine shut down rate for both aircraft and airline of no more than 1 in 20,000 hours. With ETOPS 180 that increases to 1 in 50,000 hours and for ETOPS beyond 180 that increases to 1 in 100,000 hours. If an airline short fails on maintenance and doesn't meet the required standard, their ETOPS will be downgraded or eliminated.
With that in mind, the regulatory need for 3 engine jet airlines started going away as far back as 1976, was largely gone by 1985, and by 1988 was all but dead on 95% of the routes flown by major airlines. Those previous engine out requirements were the main selling point for a three engine airliner and they offset the increased structural weight, increased maintenance difficulty, and in many cases decreased efficiency of a centerline tail mounted engine.