The thumber is an overhead throw with the thumb inside the rim to get over obstacles. Grip, flight path, disc choice, mistakes, rules and shoulder care.
The honest answer: the thumber is an emergency tool, not an everyday throw. You throw the disc overhead, similar to a baseball pitch or a chop, with the thumb inside the disc rim [1]. It flies in a steep arc upward and comes down steeply; a retailer blog describes the thumber with a "straight up, straight down" path [1]. It is used to get over trees or bushes, escape from tight lies or descend steeply and in a controlled way onto a target [1].
How rare is it? In an online survey of 883 disc golfers, 1.1% named the overhead throw as their most used throw, 86.2% the backhand and 12.7% the forehand [2]. That is a self-report from 2015, but it shows: the thumber is a specialist.
How hard is it? The movement is unfamiliar, control takes practice. There is no timeline.
The thumb presses against the inner rim, the inside of the index finger lies on the outer rim [1]. So you hold the disc such that the thumb supports it from inside (a retailer blog calls this the "thumber grip"). Try it first without throwing.
Milestone: You can hold the disc in this grip without it slipping.
The motion resembles a chop or baseball pitch above the head [1]. The disc is released steeply. In the thumber the top of the disc faces right (right-handers) [1]. Start slowly and dry.
Both overhead throws are released at a steep angle [1]. The steeper, the higher the arc. You control the speed, not the force.
Milestone: The disc visibly climbs steeply and comes down under control.
Both throws fly in a vertical arc and then pan out horizontally before fading [1]. An overstable disc pans sharper and faster; an understable one forms longer, slower arcs [1].
Before throwing, practise the motion ten times without a disc, arm loose. Then three throws at half speed in the same direction: where do they land? That shows whether your release angle is stable (practice).
Use the thumber when you must go up: over trees, down through tight gaps from above, in an emergency [1]. Check beforehand whether a simpler throw is enough.
Milestone: Of ten throws, five land in an area of 10 m × 10 m (practice measure).
Film yourself from the side and watch the release angle: the release angle decides how the disc lands [1]. A few degrees' difference changes the arc noticeably. Take ten throws with the same power and change only the angle. Note how high and how far the disc goes each time, so on the course you later know which angle you need for which gap.
An overhead throw in which the thumb lies inside the disc rim; the disc flies in a steep arc and falls steeply [1].
To get over trees or bushes, escape from dense terrain or descend steeply onto a target [1]. On open fairways it brings you no advantage.
In the tomahawk the index and middle fingers lie on the inner rim, the thumb on top of the disc; in the thumber the thumb presses against the inside of the rim [1]. The flight paths run opposite: the tomahawk turns opposite to backhand and forehand [1].
PDGA rules define a throw as the propulsion and release of a disc to change its position [6]; the rule text I read prescribes no throwing style. Stance, lie and marking apply as always.
Usually a very overstable one [1]. Overstable discs pan sharper, understable ones form longer, slower arcs [1].
Tomahawk in Disc Golf: Overhead Throw Over Tall Obstacles