The Aviation Formulary defines Clairut's formula to compute the intermediate track (bearing) for a GC based upon latitude, but any given GC (ignoring one passing through the poles), crosses a given latitude twice (below the maximum latitude where track = 270 or 90).
For my application I'd easier compute the intermediate track based on longitude, since this will have only one solution, but I'm insufficiently capable at spherical triangle math to re-arrange the available formulae to give that result. Any hints on computing immediate GC tracks based on longitude, or modifying the computation based on latitude to select the 'rising' or 'falling' solution, would be welcome.
For context, this is for a navigation device emulation in a simulator, to show the desired track along a leg. All the other values (eg, cross track error) are provided by existing formulae.