Mouse Tweaks replaces the standard RMB dragging mechanic, adds two new LMB dragging mechanics and an ability to quickly move items with the scroll wheel.
Installation
Install Minecraft Forge.
Put the Mouse Tweaks jar-file into the mods folder in your .minecraft directory.
Mouse Tweaks API

Configuration file: .minecraft/config/mousetweaks.cfg
Tweaks

RMB Tweak

Very similar to the standard RMB dragging mechanic, with one difference: if you drag over a slot multiple times, an item will be put there multiple times. Replaces the standard mechanic if enabled.

Configuration setting: RMBTweak=1

Hold your right mouse button:
RMBTweak1

Drag your mouse around the crafting grid:
RMBTweak2

You can drag your mouse on top of existing items:
RMBTweak3

LMB Tweak (with item)

Lets you quickly pick up or move items of the same type.

Configuration setting: LMBTweakWithItem=1

Hold your left mouse button to pick up an item:
LMBTweak1

Drag your mouse across the inventory. Items of the same type will be picked up:
LMBTweak2

Hold shift and drag. Items of the same type will get "shift-clicked":
LMBTweak3

LMB Tweak (without item)

Quickly move items into another inventory.

Configuration setting: LMBTweakWithoutItem=1

Hold shift, then hold your left mouse button:
(Mouse cursor is not visible for some reason)
LMBTweakWithShift1

Drag your mouse across the inventory. Items will get "shift-clicked":
(Mouse cursor is not visible for some reason)
LMBTweakWithShift2

Wheel Tweak

Scroll to quickly move items between inventories. When you scroll down on an item stack, its items will be moved one by one. When you scroll up, items will be moved into it from another inventory.

Configuration setting: WheelTweak=1

Configuration setting: WheelSearchOrder=1

When you scroll up, the mod will search for items from last to first (when this is set to 1) or from first to last (when this is set to 0).

Configuration setting: WheelScrollDirection=0

Set this to 1 to invert the default scroll actions. So, when set to 1, scrolling down will pull the items and scrolling up will push the items.

Set this to 2 to enable the inventory position aware scrolling. Scrolling up will push the items into the other inventory if it's above the selected slot, or pull items from the other inventory if it's below the selected slot. Vice versa for scrolling down.

Configuration setting: ScrollHandling=0

Toggles between "smooth scrolling, minor issues" (0) and "non-smooth scrolling, no issues" (1). When set to smooth scrolling, minor issues may be experienced such as scrolling "through" JEI or other mods. When set to non-smooth scrolling, those issues will not happen, but the scrolling will be a little non-smooth. Non-smooth scrolling works only with the Forge OnTick method.

This option is set to smooth scrolling by default because the aforementioned issues require rather specific conditions to trigger and aren't very impactful, while scrolling items is something you do all the time and want the experience to be as good as possible.

Compatibility

Mouse Tweaks is compatible with everything based on GuiContainer (as long as the behavior isn't changed too much).

If your GUI isn't based on GuiContainer, or if you want to improve compatibility (making Mouse Tweaks ignore some slot, for example), take a look at the API Description.

Thank you to YaLTeR for creating and maintaining the original mod. See https://www.curseforge.com/minecraft/mc-mods/mouse-tweaks for the original mod and for versions outside of 1.12.2.

Feel free to include Mouse Tweaks in modpacks. If you want to list a download link to the mod, please use the CurseForge link so it counts towards the download count.

Installation

Tweaks

RMB Tweak

LMB Tweak (with item)

LMB Tweak (without item)

Wheel Tweak

Compatibility

Mouse Tweaks Unofficial