With the particular modpack I am playing, there is a softlock involving technology unlocks and graphite. It appears that the minimum set of mods needed to create this softlock is Graphite & Diamonds, Vanilla Galore Continued, Lignumis, and Wooden Industry.
Specifically:
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Mining graphite requires an electric mining drill.
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Crafting an electric mining drill requires electronic circuits. (Recipe is modified by Vanilla Galore Continued then by Graphite & Diamonds.)
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The Electronics research has a prerequisite of Graphite Processing, which requires graphite to be mined. (Research for electronics is modified by Lighted Electric Poles +, then Vanilla Galore Continued, then by Lignumis, then by Graphite & Diamonds, then by Wooden Industry. Research for Graphite processing is only modified by Graphite & Diamonds.)
My guess to the cause of this is that perhaps Graphite & Diamonds intends for the burner mining drill to have fluid input, which would allow the burner mining drill to mine graphite, which would resolve this loop. However, the MiningDrillPrototype setting of "input fluidbox prototype" is empty, and the drill is not placeable on graphite. If I try to place the drill, I get the message "Burner mining drill cannot mine this resource".
In my playthrough, I got by this deadlock by cheating in an electric mining drill to mine the graphite, which unlocked the trigger technology and also allowed me to create electronic circuits to create more electric mining drills. In case it would be helpful, I have uploaded my save and the custom mod I made for this save on Google Drive here: https://drive.google.com/drive/folders/1jtj-XJLnRFt6NxfiEs3II3hWkZ-S7ISl . Note that this save is past the point of the deadlock, but may still be useful for syncing mod settings and looking at prototypes, etc.
(Edited for formatting)