Something to remember but the Thatch weave is a defensive maneuver. Also, consider that ACM training during WWII was a mixed bag usually left up to the squadrons and therefore, you were very likely to have a very inexperienced wingman. The weave is a simple tactic requiring only basic knowledge and is suitable for any wingman to perform. It's basic function is to get both fighters out of phase with each other, i.e., they're turning different directions which allows the free fighter to obtain a shooting position. Also, the US planes had less maneuverability than their opponents, this maneuver counts on the Japanese belief that once on someone's six the situation was almost impossible to reverse so the tactic is designed to provide shot opportunities for the free fighter, particularly when the bandit is boresighted on the other fighter.
Some things to think about:
First, it's never a good idea to intentionally put yourself on the defensive. That being the case, an initial cross turn is usually the best response to a bandit closing on the section's six, so the first step is pretty much automatic regardless of the bandit's distance. If sufficient distance exists (probably outside of 2k) between the fighters and the bandit, a full 180 cross turn (one fighter goes high and the other low) will get both fighters facing the bandit and neutralize his position advantage. When the bandit chooses the fighter he's going to attack that fighter becomes the "engaged" fighter and the second is "free". The free fighter's job is to position himself for a shot (while watching for the bandit's wingman) while the engaged fighter's role is to make the bandit predictable either by "pushing" or "dragging" him toward the free fighter.
If insufficent distance exists to complete a 180 cross turn (inside of 2k) this is where the weave comes in. The fighters still turn into each other but then reverse their turns to begin the weave. The engaged fighter is "defensive" and the free fighter needs to go on offense. Assuming the bandit isn't actually pumping out rounds, the free fighter's job stays the same and he needs to quickly get to a good shooting position. He has a few options. If the separation is great or the bandit has lots of e the free fighter can do a low yo-yo to cross the circle, gain speed and close the distance. If separation is relatively small, the free fighter should assess the angles, and can do a high yo-yo or lag roll to put himself on the bandit's six. If he's presented with a lot of angles and a potential forward quarter shot opportunity he needs to assess the threat to the engaged fighter. If the engaged fighter is still outside of the bandit's gun range then the free fighter should choose a positioning maneuver such as a high yo-yo to put himself on the bandit's six. If the engaged fighter is very defensive and in danger of being bagged in the next few seconds than the free fighter should go for the forward quarter snapshot (yeah, yeah, yeah....maybe even a HO). The problem with going to the snapshot is that the free fighter is giving away angles for a low percentage shot and, should he miss, it'll take more time to get on the bandit's six than if he just went for the positioning maneuver first.
Going back to the initial setup, if a bandit is spotted very close and is already in a shooting position on one of the fighter's six then both fighters should break turn toward each other. Even a forward quarter snapshot by the free fighter will usually work to at least distract the bandit. Following the snapshot both fighters should reverse their turns and give the free fighter another opportunity for a shot. This would be a very tight, high-g weave.
A couple of other notes, the weave does work in the vertical and also in the oblique, it doesn't have to be flat. Also, both fighters should never be co-alt at the start (but still within 2-3k). Different altitudes complicates the bandit's problem since the fighters are both out of phase and out of plane.
