GA flight instructor with student reported an NMAC while in the pattern of MEV non-towered airport requiring evasive action to avoid a possible collision.

Narrative

While doing pattern work with a student on Runway 34 at MEV; an inbound aircraft; Aircraft Y; made a traffic call indicating that they were about 3 miles out; descending; and intended perform a standard forty-five degree entry to the downwind. We had just turned crosswind; made a position report; and discussed the importance visually identifying the inbound traffic. After reaching traffic pattern altitude on the crosswind leg; we continued to visually scan for the traffic. The traffic could not be visually identified; and a downwind turn was initiated; along with the radio call; 'Minden traffic; Aircraft X turning left downwind Runway 34; Minden traffic.' During the left turn into the downwind leg; I was; fortunately; able to spot the aircraft out the right window of the cockpit. The aircraft was at our altitude; at what appeared to be a very high rate of speed; and seemed to be initiating a right-hand turn to intercept the downwind leg. The trajectories of each aircraft and the very high closure rate indicated to me that a collision was imminent; perhaps within approximately 2 seconds. I grabbed the control wheel and initiated an abrupt; rapid climb and was able to climb to approximately 100 feet above the inbound aircraft; which passed directly beneath us a second later.The rest of the flight was conducted without incident.In my opinion there are 3 main factors which contributed to this near miss:1) The speed at which the inbound traffic was entering the traffic pattern - It seems likely that approaching at such a high rate of speed does not allow for proper visual scanning or coordination/deconfliction with other traffic already established in the traffic pattern.2) The failure of the pilot to adhere to the guidance provided in AC 90-66C regarding proper uncontrolled airport traffic pattern entry - This AC states clearly that 'Entry to the downwind leg should be at a 45-degree angle abeam the midpoint of the runway to be used for landing.' Had the pilot of Aircraft Y entered the downwind leg at the recommended midfield point; there is a much greater chance that visual contact could have been made and the overall risk could have been reduced or completely mitigated. 3) Failure to use aircraft lighting - The pilot of Aircraft Y did not have his forward-facing lights on during the pattern entry. Had the landing; taxi; and/or recog lights been turned on; there would have been a much greater chance of early detection and deconfliction.In my opinion; a lack of familiarity with FAA guidance on uncontrolled airport operations and best practices is at the heart of the issue. Perhaps instructors and examiners could emphasize this issue more strongly; or perhaps the FAA could mandate that this be included in the Flight Review.