After trying vanilla hoppers, pipes from the "Pipes" mod by CrafterKina, hopper ducts from the "Hopper Ducts" mod, hopper pipes from the "Faucets and Filters" mod, and tubes from the "Simple Tubes" mod... I'm beginning to suspect the issue may be coming from Storage Drawers itself, so I've decided to create an issue for it - sorry if I'm wrong, though. None of the types of transfer methods I've tried have been able to pipe things into the storage drawers.

Minecraft 1.12.2 singleplayer
Forge 14.23.2.2629
Storage Drawers 5.3.5

Vanilla hoppers work. They will insert and extract.

Ok, thanks, I'll have to give it another go with the vanilla hoppers. I'm pretty sure I tried but it could be that, at the time, one of the mods I was using maybe changed vanilla hoppers behavior and made them not be seen as vanilla hoppers or something.

Hopper Ducts is the only one I've heard of out of that set.

Taking a quick peak into the Hopper Ducts jar, it looks like it still only interacts with the old Minecraft IInventory interface, instead of supporting Forge's newer IItemHandler from the past few Minecraft versions. SD only supports the later, so Hopper Ducts is not compatible with it.

It could be that the other mods fall into the same boat, but I'd actually have to check their source to see.

SD works with other mods like Thermal Dynamics, Refined Storage, AE2, etc.

Hmmm, ok, could be I just had really bad luck with the mods - but are vanilla hoppers not meant to work with the drawers? I can't remember if they used to or not.