Hi everyone,
I'm the OP, thanks for the numerous replies (for some reason I didn't get notification there are posts, usually I do!).
So, I recently installed a sequential LED taillight, but the plate bulb burning was noticed even before, with the regular taillight that had no mods whatsoever on the rear. It's really confusing, but I should probably follow some of the advice you've given me (voltmeter measurements, etc.) and see where the problem lies.
Hope I get around to doing so soon, will write if I find the problem!