Yes you use the compressor clutch activation wire to activate the relay. An in-line relay is just a normal automotive relay used in close proximity - placed in the engine compartment in this case. It also implies a serial connection - but that makes no sense here - miss-used term.
I'd suggest you use a weather sealed 30A SPST or SPDT relay like a hella:
Easy to mount and use - Screw the case to something and wire using the pigtail - use 12 AWG wire.
See if pelican has them.
You can just connect this relay in parallel with the exisiting fan relay to drive the fan (via terminals 30 & 87) power it from the jump post (on 30) and connect to the fan motor power terminal directly (on 87).
Connect the coil to the compressor clutch wire (86) and also to the starter solenoid signal (85) connect this to pin 14 (Yellow wire) on the 14 Pin connector @ jump post. You can use 16AWG wire for just these 2 connections.
You don't need a diode unless you plan to use only the existing relay.
Operation: fan works as normal - except it also comes on whenever the compressor is on (this is only active when ignition is on). This also turns the fan off when the starter activated - this is what you need.
There is a different modification to protect the small AC clutch relay in the head unit in later models - you don't have this - you have a switch in the head unit for the AC Clutch relay - so no need.
Alan