I used a lawn mower size battery for my situation but again, it was only "carrying" the load of the GPS system while the tractor was started. The controller that it was working with was shut off over night.

While I was actively using the entire system when planting, the tractor charging system was charging the regular tractor batteries (2-12V in parallel) as usual.  A wire connected them through a diode to the the small battery in the corner of the cab.  A Trimble 332 was connected to the small battery. 

In general, a diode can be thought of as a one-way check valve. A diode has many similarities to a check valve in a water system. It allows flow in one direction with a slight restriction but prevents flow in the opposite direction.  The direction of attaching the diode is important.

Thus the tractor batteries charged the small battery when their voltage exceeds the voltage of the small battery but prevents discharging when the voltage of the tractor batteries is less than the voltage of the small battery.  Since there is some voltage drop across the diode, the voltage in the small battery was less than the voltage of the tractor batteries but was within the acceptable input voltage range to the GPS.

The GPS was left ON day and night during the planting season.  The tractor/planter were parked in an open area overnight.  When the tractor was shut down overnight, the Ag Leader Insight controller and Nav II were powered down.  But since the GPS was powered from the small battery which in turn was connected through the diode to the tractor battery, the GPS received power over night.  The small battery didn't become discharged since it was still connected to the tractor batteries.  Left this way for many days the GPS might eventually run the tractor batteries down to an unacceptable level.  This would not happen with the more deluxe arrangement suggested by the poster above.  It was not an issue for me since I was only doing this during the planting season where the tractor was usually restarted every day. 

The next morning when I started the tractor, the starter might reduce the voltage on the tractor batteries temporarily during the starting process.  But the diode connecting the tractor batteries to the small battery prevented the voltage in the small battery from reaching the lower critical level where the GPS and Omnistar Convergence would drop out.

As soon as the tractor started, its charging system would again start charging the tractor batteries which in turn would recharge the small battery the small bit it had discharged.

When planting season was over, I would shut off the GPS.  Then there was no load on the small battery and the regular tractor batteries would not be drawn down.  When I wished to use the GPS again, I would turn it ON and I did need to wait for the Convergence process to complete.

Now that I use an Ag Leader GPS 7500 with Terra Star Pro C, the convergence issue time has been reduced significantly.  I do need to wait for the system to acquire the raw GPS fix and then converge to an acceptable level each morning.  However, the amount of time delay is very acceptable so I no longer use any type of small battery in the cab.