Not People skills
AS an AMT or AME,
It is more of politics,
Yes we all have customers but other than your MGR, Pilots like to be told what they have as a product, no B/S selling, no offence to listening pilots but in my experience they like to hear a confident, matter of fact and somentims commanding explanation of the condition in wich the aircraft they are flying is in. Details that prompt questions result in delays.
Ground ops people need to be delt with in a more ambiguious manner unless you know for a fact you are airworthy or not depending on the airline.
Do you need good people skills as an engineer?
This environment is like none other I understand.
I would short sell you not to say that you need people skills in any career.
In the other life of phase maintenance, performing step by step routine tasks much like a factory environment you really do not need to deal with anyone but your lead/chief or supervisor. You could live quite content doing your 8/10 or 12 hr shift with minimal human interaction.