there is a 2 prong connector beside the cdi/reg rectifier connector....it supplies the signal from the spark sensor next to the stator.....it is not uncommon for the wires inside to become "de-pinned". look that connector over carefully...it could be plugged together , but one wire may have been "de-pinned" and is no longer located in the connector.
From your description of the coil wires, you have an EFI machine. 2008 is not efi..so don't use the 08 cdi...as that should be a carby...shouldn't even "plug up".
you won't get a coil reading unless the computer is supplying pulses to the coil...
The coil will say GT650 efi and have either an "F" for front cylinder or and "R" for rear cylinder. The "F" coil will work at both locations....the "R" believe it or not , is constructed cheaper and fails quicker.
the stator connector and spark control connector are underneath the seat frame, and you can see them after removing the cover that holds the seat release. they are usually inside a rubber wrap that looks like a blob with a chunk of rubber over them.
1100 miles is the magic number to have a cooked (discolored) stator connector and crumbly and de-pinned spark control connector