I have been toying with this idea for a little while and what i have dreamed up differs from your desire slightly.
The third move will bes seperate from the existing two. It will not influence energy and have its own timer for use. I have not decided if every move will have a unique timer or the cooldown will ve universal.
These new moves will not do damage. Each pokemon will gain one stat (boosting or hindering) or status affliction move. By incorporating moves like WilloTheWisp, Dragon Dance, Tail Whip, Toxic, and so on, i believe would be a step in tge right direction for revamping the current combat system.