Many thank you to Ed Stockly for helping me out with my first phase of an Adobe Illustrator relink script. With his help, the script is able to change the link location between three different libraries. There is a high resolution connected server library, a low resolution connected server mirror library of the high resolution (with minor change in folder hierarchy) and lastly a connected USB version of the low resolution library.
set BoxSync to (path to home folder as text)
set LoResLink to "CG Master_LR"
set HiResLink to "CG Master_HR"
set NewExt1 to ".tif"
set NewExt1Small to "-sm.tif"
set ErrorList to {}
set LinkInspect to {}
tell application "Adobe Illustrator"
activate
set user interaction level to interact with all
display dialog "Please chose link mode" buttons {"HiRes", "LoRes", "Box Sync"} default button 2
if the button returned of the result is "HiRes" then
set ErrorList to ErrorList & my LinkSwitch(document 1, LoResLink, HiResLink, 3, NewExt1)
set ErrorList to ErrorList & my LinkSwitch(document 1, BoxSync, HiResLink, 5, NewExt1)
else if button returned of the result is "LoRes" then
set ErrorList to ErrorList & my LinkSwitch(document 1, HiResLink, LoResLink & ":Assets", 2, NewExt1Small)
set ErrorList to ErrorList & my LinkSwitch(document 1, BoxSync, LoResLink & ":Assets", 5, NewExt1Small)
else
set ErrorList to ErrorList & my LinkSwitch(document 1, LoResLink, BoxSync & ":Box Sync:Assets", 3, NewExt1Small)
set ErrorList to ErrorList & my LinkSwitch(document 1, HiResLink, BoxSync & ":Box Sync:Assets", 2, NewExt1Small)
end if