I don't think the mode shifter is involved in this problem, assuming I understand its function, which is changing the drive mechanism between agitation (only the impeller rotates) and spin (the basket and impeller are locked together so both are driven by the motor).
I suppose a key to the diagnosis is whether the motor is reversing during agitation as it should be, or turning in only one direction.
If the motor is reversing but the impeller is not, then the transmission may be at fault.