Just wanna know if I should collect more information and file a proper bug report.
Have a pack that adds emissivity to Malum's Brilliant Stone, but when I have CTM installed, Continuity's system doesn't appear to trigger.
This is what shows up with CTM:

This is what shows up without CTM:

Is there any way to get them to work at the same time so that the block both gives off light (CTM) but also renders pixels in fullbright (Continuity)?

CTM does not do that. Its definition for light only affects the minimum lightmap value of quads which use the corresponding texture, which is similar to what Continuity's emissives do.

My mistake. I was trying to distinguish the effects of the two mods' emissivities.

Continuity has no integration with the CTM mod. This is a bug, and I do not know the cause of it.

Chisel-Team/ConnectedTexturesMod#246

Only Continuity:

Logs: https://gist.github.com/CraftyZombie/d92ba91709d7d7097e7eeb9e45996771

Both Continuity and CTM:

Logs: https://gist.github.com/CraftyZombie/e460089fc8802346b55d12fcd81248f1

...the block both gives off light (CTM)..

CTM does not do that. Its definition for light only affects the minimum lightmap value of quads which use the corresponding texture, which is similar to what Continuity's emissives do.

One possible reason for why this issue happens is that CTM is wrapping Continuity's model instead of the other way around. This would completely disable connected or emissive textures defined through Continuity for that block/item. If this is the actual cause, then CTM can change that if they wish, but that is more of a Connector/Forgified Fabric API bug than a CTM bug or Continuity bug. However, fixing it would be quite difficult.