Right advice. Different manufacturers have different ways of connecting their shift rods. Not sure how Mercury does it. On other outboards I've dropped lower units, by disconnecting the shift rod after removing an access plate. The rod had a coupling under the access plate. Then it took some jiggling around to reconnect everything right.
Also, if the lower unit has not been removed from a while, things might be stuck and some force required, but be careful, don't want to crack the casting. Don't ask how I know.