This is a pic of my re-assembled steering assembly. There are three zerks: one in the foreground on the cable clamp, one just past that one the steering cable, and in the distance there's one on the rudder shaft housing.
When I dropped the rudder I found that there is very little extra room in there. The shaft is 1 1/8", and the housing is just a few thousandths bigger. Mine has upper and lower O-rings, and they seal very well. In other words, you just can't pump more grease into it as you would a wheel bearing; there's no place for it to go.
You can see the tiller arm on top of the shaft, and the clamping bolt on the right side of the picture. The bolt had to be completely removed, not just loosened, before the tiller arm came off.
I would venture that you can't pump more grease into the zerk because the system is already full of grease. When my zerk broke off I found that it was corroded, so maybe you want to replace yours. It would be easy to do, just unscrew it. I bought some new zerks, got ten for $6.50. (This will be a lifetime supply for me!)