Why? I wish the vacuum shift on the FJ62 was as reliable as the one on 40 series with the one piece transfer case. While this one is older the dash setup on the 68+ a is very clean setup. You want to run 2WD low just a matter of removing a pin on the high/low shifter.
Yes, rubber boots. Still available. Toyota 36426-60010 and 36318-60010. The cavity where the shift fork is will get gear oil from the transfer case, but putting some in there before putting back on TC is good. The gasket for the mount is also still available, don't have the number though. The nut on top is for access for oiling the pneumatic shaft, light oil of some kind. Have you checked the vacuum functionality of the unit? If not, put a 3/8 hose on each inlet and suck, one side should pull the shaft in, the other will push it out. If that doesn't work, you'll need to disassemble and assess the issue - maybe the diaphragm, maybe a leak (o-ring referenced above), maybe needs cleaning, or all of the above.
Land Cruiser Vacuum Transfer Shift Assembly, Lever Assembly, Vacuum Switch Assembly, Diaphram Assembly, Vacuum Diaphram Assembly, Vacuum Switching Valve
While you have it out you may as well order all available parts and rebuild it.It is an easy process.
A diaphragm,if needed, can be cut from a piece of fabric reinforced rubber of the correct thickness-available from Mcmaster-Carr.
Pretty good chance the existing diaphragm is fine.Dawn dish soap and/or any Gojo type citrus based hand cleaner works wonders on cleaning and restoring rubber.