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Wiring the Cornering Light to always be on when you turn on the City Light question.

The Left Cornering Light wire color code is Positive = Red/Green and Negative = White/Black
The Right Cornering Light wire color code is Positive = Pink/Yellow and Negative = White/Black

Pink/Yellow gets T-tap to Red/Green and goes to an Automotive 30 amp Relay pin out #87
White/Black gets T-tap to White/Black and goes to the Battery's Negative Cable Connector
From the Battery's Positive post, it goes through a Inline Fuse holder 30 amp fuse to the 30 amp Relay pin out #30
To ground the 30 amp Relay, run a wire from the Battery's Negative post to the 30 amp Relay pin out #85
To turn on the Cornering lights afterwards while turning on the city light, Run a wire from 30 amp Relay pin out #86 to the 12 volt wire on the City Headlight Switch.

Does that all seem about right?

I'm looking at OnDemand5 Wiring Diagrams for the 1992 Lexus SC300.