I'd suggest a call to a Tohatsu dlr. And ask if that delay shift characteristic is typical.
Usually the joining clamp is visible when the lower unit is unbolted, and dropped an inch or two (which is the travel of the shift lever and rod). If its sliding you should see witness marks on one of the shafts. The shift lever won't be straight up and down when in neutral.
As I said, I've had outboards apart but never a tohatsu.