The '
rod which attaches to the steering arm linkage and goes through the tube on the engine doesn't move when pushed or pulled' is the business end of the steering cable. With the retaining nut on the starboard end fully undone & the steering arm detached from the port end the whole cable should just pull out. Loosen the nut on the port side as well & see if you can now pull the complete cable from the engine. If you can't, its seized to the tube & you will have to try & free it off with penetrating fluid. Be very careful if you try & hammer it out as you may expand the end & it then won't go though the tube, meaning you'll have to cut it off & buy a new cable.
Not the best, but this link should help you see how the helm end works on your steering helm:
Another one here:
Once the cable is released from the tube try & turn the wheel. If the cable end then moves freely in & out clean the end and the tube - I use a shotgun cleaning phosphor bronze brush - lubricate & refit. If the steering tube is very corroded/rusted an expanding reamer may be of help, but only use it to clean not to enlarge the hole.
DO NOT try to loosen a seized cable by forcibly turning the wheel. The insides of the steering helm are alloy and you WILL break it leading to having to buy a new one.
ETA. With the starboard sized nut removed does the wheel now turn & the cable outer move freely? If it does then the cable is OK & it's just the end seized in the tube.