Boeing recommend that when on automatic pilot, the PF should make the AFDS mode selections. The PNF may select new altitudes if crew duties permit. Boeing fail to differentiate between two engine on autopilot and one engine inoperative on autopilot.
However, you need to take into account the situation when flying on autopilot with one engine inoperative. Here you have manual rudder, and manual thrust lever.
To expect the PF to operate the AFDS as well as adjusting manual rudder and its rudder trim, plus manual thrust lever changes, is unrealistic.
Common sense dictates in the case of one engine inoperative on automatic pilot, the PNF should operate the AFDS. Boeing seem to ignore this type of situation. So do the pedants