I'll be damned if I can find what is specifically called for right now, but suffice to say it needs to be something that won't go all loose/drippy when it gets hot.
One could even use a very small dab of high temp bearing grease that's specifically for disc brake setups. (you know, the stuff you'd use on the front wheel bearings)
Super high temp lithium would also be serviceable.
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Query:
Do you have the rubber 'pocket' as shown in the thread you linked above in
this specific post? (p# 10541.12413.00)
That is there to help hold the lube onto the ball-n-fork contact surface and also doubles as a sort of dust boot to help keep grubbins from getting in and increasing wear.
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Regarding the pilot, if you've not installed it yet you might want to impregnate it with oil before doing so. (it's not even really required, but more a 'peace of mind' thing, if you worry about such things

)
If you grease it, go VERY sparingly as (1) any that gets squished out can sling pretty easily and (2) get too much in there and it can actually pop itself out as the pilot shaft of the trans is pushed in.