Many old Kay-made banjos use the "single coordinator rod" system seen above and have a metal or plastic adjustable neck-angle bracket that supposedly lets you set action sort-of on-the-fly. I've found a number of flaws in the design and these days I have no patience with setting-up these banjos unless I fix the flaws.
Here's the neck angle bracket. It's curved and if you loosen tension on the neck at the big bolt in the rim...
...you can swivel the neck angle back and forth. The first thing I do on a rim like this is just that -- set the angle I want (usually to get a 5/8" bridge on the head and 1/16" action at the 12th fret) and then tighten-up that ginormous bolt as much as I feel I can before endangering the heel.
The next thing I do is pre-drill a hole to fit a drywall screw directly through the rim, metal neck angle block, and into the heel. I then find an appropriate washer, screw, and slam this "bolt" home.
This solves two things that are trouble with the design -- the tendency for the neck angle to shift as the banjo moves about (or is tensioned-up for that matter), when it encounters different weather, and when the bolt loosens up. The second thing it does is securely keeps the neck from rotating left or right. The plate has an alignment groove in it to supposedly hold the neck in one plane, but it doesn't really work too well.
So -- the neck joint is now tight and secure. On to...
...the other side of the coordinator rod. It terminates in a hex nut on the inside and the endbolt on the outside. A coordinator rod is a lovely thing to have in a banjo, as small adjustments to it (tightening from the outside = lower, loosening from the outside and tightening on the inside = higher) will allow you to set action without having to do any other adjustments on the instrument.
The problem here, of course, is that one of the "adjuster nuts" is actually the endbolt, so I need to move that.
Here I've drilled a new, lower, hole and installed a parts-bin "shoe" to replace the old endbolt. I've then added another nut for external adjustment.
With the tailpiece installed one can still get at and turn the nut with pliers or wrenches.
The other big failing of older banjos is friction pegs, so I replaced the original friction pegs with 4:1, cheap, geared tuners. These are about $24-25 on eBay and come with god-awful buttons, so I tend to replace them with plain white or black plastic ones.
As a side-note... plectrum banjos with their long 26-27" scale lengths (this one has a 27 1/4" scale) need quite light strings to keep the old unreinforced necks happy. I'm using a "light" 5-string banjo set minus the extra 9 (for the drone G) for tuning this to DGBE in "Chicago" tuning. The same set works for CGBD -- standard plectrum tuning.