On F chords while playing acoustic, as well as in several Gaslight songs, Brian will play what I like to call a -6 chord. This involves playing a full barre chord, but leaving off the 6th string.
A full F chord, normally played like this:
e|-1-|
B|-1-|
G|-2-|
D|-3-|
A|-3-|
E|-1-|
would be played like this, as an F(-6) chord:
e|-1-|
B|-1-|
G|-2-|
D|-3-|
A|-3-|
E|---|
The same rules apply for forming minor -6 chords as it does for full barre chords. An Fm(-6) chord would be played like this:
e|-1-|
B|-1-|
G|-1-|
D|-3-|
A|-3-|
E|---|
Also, while playing live or acoustic, and most likely on the albums, though I can't be certain, Brian forms his standard G chords like this:
e|-3-|
B|-1-|
G|-0-|
D|-0-|
A|-2-|
E|-3-|
This also applies to F chords played when tuned down a whole step, as most Gaslight songs are played. An F chord played down a whole step looks like a G chord, and Brian plays this with the above formation
And if you couldn't tell, all Gaslight songs are played live tuned down a whole step, though this is not always true for the albums. The Navesink Banks and Here's Looking At You, Kid are played down just a half step, though they are played live down a whole step to avoid having to retune during the show. Red At Night is played in standard tuning on the album, but is played down a whole step live, for the same reason.