New Process shifter questions

Friends-
I have completely disassembled and cleaned the shifter for CUDAVRT's newly rebuild a-833. Should the shift mechanism inside the lower boot be lubricated or left dry? If so, what kind of lube?

The engine and transmission are on the K member and on the stand (borrowed from a friend who restores Road Runners, etc.). I will remove the shift linkage before the install from below, using my 2-post lift.
Thanks,
Stroker

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