Ver. 1.7.10, Forge 10.13.4.1614
Tested CB Multipart 1.2.0.345 & GTMEGA Multipart 1.6.2.
FalseTweaks 3.8.3

Placing multiple torches, etc. into the same block space immediately turns each block invisible. When removing FalseTweaks, the problem disappears. I couldn't find a duplicate issue, but saw that there were modified versions of Multipart, so I tried the GTMEGA version and had the same results. Let me know if it's a problem on my end!

You should use the GTNH forks of CodeChickenCore, MRTJPCore, Multipart, Relocation, and ProjectRed (if you have them). The MEGA ones are only maintained for our modpack, but the GTNH ones also have threaded rendering safety patches, and they're open to fixing compat with third party modpacks in their mods.
Make sure you also delete the CodeChickenLib jar from mods/ or mods/1.7.10/, their CCCore ships with CCLib built-in.
you can find the gtnh versions of these mods here:
https://github.com/GTNewHorizons/CodeChickenCore
https://github.com/GTNewHorizons/Mrtjpcore
https://github.com/GTNewHorizons/ForgeMultipart
https://github.com/GTNewHorizons/ForgeRelocation
https://github.com/GTNewHorizons/ProjectRed

@FalsePattern In FalseTweaks version 3.9.0, torches are rendered transparent when multithreading is enabled. I am using the GTNH version of ForgeMultipart.