Lexs400

I am diagnosing a brake issue and while doing that the question of the type of master cylinder came up. I would like to know if the type used in a 1993 LS400 with trac. is a "quick take up master cylinder" or the regular non "quick take up master cylinder". The reason for that is because the pedal is low and mushy and the only two situations that I've come up after following the flow chart below is either "air in the callipers or a faulty "quick take up master cylinder".
I would also like to know how I can get rid of air in the callipers. I've done regular bleeding as described in the service manual multiple times but that didn't help.