I usually use Sta-Lube (you can't find any locally?) My local carries GL-3 and GL-5.
A synchroniser is a mechanical device, but doesn't depend on cluches - therefore, doesn't require friction modifier. The main issue with GL-5 is that the added sulphur and the heat of operation will work together to dissolve the sintered bronze synchroniser rings.
Granted, I woudln't use Pennzoil in a lawnmower, but I've had too much history with it in engines to like it. It would probably be less problematic in a transmissions, but you'll want to run some solvent when you get some new oil to clear it out.
Since you're planning on replacing it anyhow, is it internal slave, or external? I'm digging around for an external slave front end for an AX-15 (bellhousing, fork, front bearing retainer...)