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.