I have a question based around a FAQ post, as well as the Advanced Weapon Training (AWT) feat in the Weapon Master's Handbook.
First, the relevant FAQ: http://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9qto
Archetype: If an archetype replaces a class ability with a more specific version of that ability (or one that works similarly to the replaced ability), does the archetype's ability count as the original ability for the purpose of rules that improve the original ability?
It depends on how the archetype's ability is worded. If the archetype ability says it works like the standard ability, it counts as that ability. If the archetype's ability requires you to make a specific choice for the standard ability, it counts as that ability. Otherwise, the archetype ability doesn't count as the standard ability. (It doesn't matter if the archetype's ability name is different than the standard class ability it is replacing; it is the description and game mechanics of the archetype ability that matter.)
Example: The dragoon (fighter) archetype (Ultimate Combat) has an ability called "spear training," which requires the dragoon to select "spears" as his weapon training group, and refers to his weapon training bonus (even though this bonus follows a slightly different progression than standard weapon training). Therefore, this ability counts as weapon training for abilities that improve weapon training, such as gloves of dueling (Advanced Player's Guide), which increase the wearer's weapon training bonus.
Example: The archer (fighter) archetype gets several abilities (such as "expert archer") which replace weapon training and do not otherwise refer to the weapon training ability. Therefore, this ability does not count as weapon training for abilities that improve weapon training (such as gloves of dueling). This is the case even for the "expert archer," ability which has a bonus that improves every 4 fighter levels, exactly like weapon training.
The second relevant part is the Fighter Brawler archetype, which replaces Weapon Training 1 and 2 with:
Close Combatant (Ex): At 3rd level, a brawler gains a +1 bonus on attack rolls and a +3 bonus on damage rolls with weapons in the close weapon group. Both of these bonuses increase by +1 for every four levels beyond 3rd (to a maximum of +5 on attack rolls and +7 on damage rolls at 19th level). This ability replaces weapon training 1 and 2.
The Advanced Weapon Training Feat requires Fighter Weapon Training as a prerequisite and from reading the FAQ and looking at the wording on the brawler archetype ability it looks like Close Combatant would qualify. Regardless, I wanted to get another opinion on if it would.