As shown in the picture, the Forge dynamic bucket (and the bucket from my mod which uses the same model) has Z-fighting when rendered on a drawer.

Using Storage Drawers 1.10.2-3.5.7 and reproducible with only Storage Drawers installed.

I wonder if it's a case where the forge icon will render reliably in a perfectly head-on display (the GUI) but not at off-angles as you see in the world. I'm not sure I can do anything to fix that.

Maybe something goofy like rendering the item icon to an offscreen texture, and then drawing that onto the drawer.

Are most or all mod buckets derived from dynamic (the items all appear to be attributed to MinecraftForge)? I just tested a bunch and I didn't see any Z-fighting.

Historically I've seen Z-fighting become an issue in the presence of Optifine.

Yeah, just about all fluids these days use the forge bucket, though note that in a fresh Forge install it is disabled by default, mods like Tinkers enable the Forge switch so it remodels vanilla fluids as well (there is a boolean in the Forge config file to test it without Tinkers). From what I know from a similar case, it comes from quads not being perfectly aligned after transformations, but it is odd that it happens on buckets and not vanilla multilayer items then.

I never use Optifine, just about every other update breaks something simple in Tinkers Construct or Immersive Engineering, leaving me to just avoid it.

Yup, having this issue too. I'm not using Optifine.