
chaoseffect |

I have no RAW answer for you, but I see it as going one of two ways:
1. Unarmed strike has to be your primary attack as it is what gives you Two Weapon Fighting and from there you may use whatever as an offhand.
2. If you choose to use Greater Brawler in a particular round, you are locked in with unarmed strikes as both primary and offhand attacks, so no longsword at all allowed in the rotation.
I would be inclined to say 2 is the way it works, but in a home game I would see no issue with going 1.

Claxon |

They way I would run it, is that you only benefit from Greater Brawler when you use only unarmed strikes.
Attempts to use other weapons would mean you use two weapon fighting without any of the appropriate feats.
Two-Weapon Fighting
If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon. You suffer a –6 penalty with your regular attack or attacks with your primary hand and a –10 penalty to the attack with your off hand when you fight this way. You can reduce these penalties in two ways. First, if your off-hand weapon is light, the penalties are reduced by 2 each. An unarmed strike is always considered light. Second, the Two-Weapon Fighting feat lessens the primary hand penalty by 2, and the off-hand penalty by 6.

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1. Unarmed strike has to be your primary attack as it is what gives you Two Weapon Fighting and from there you may use whatever as an offhand.
2. If you choose to use Greater Brawler in a particular round, you are locked in with unarmed strikes as both primary and offhand attacks, so no longsword at all allowed in the rotation.
Personally I think RAW says #2. Some may believe RAW says #1 or other similar interpretations.
Ultimately ask your GM is all we can tell the OP. The rules don't clearly cover this situation.

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So normally your penalties for fighting with a light off-hand and a regular weapon is -4 (Primary) -8 (Secondary). Two weapon fighting improves the primary by +2 and Secondary by +6. You count as having two-weapon fighting with unarmed strikes; but not longswords. Therefore, RAW you would get the bonus with the hand and not the longsword; making your total penalties -4 to hit with longsword and -2 with your fist.