Good news!
I not only found the spare connector I had, I actually already had it wired for when I had my CBR track bike so that I had a connector on each bike in order to not have to keep switching them out depending on which bike I was riding, but when I sold the CBR I took the adapter off.
You can see in one of the picture the connector that the lap timer comes with and the male counterpart that it plugs into (the yellow one). That's the one I had to buy and I just spliced it to a standard connector that battery tenders use, and I know for sure that all these bikes come with one from the factory (should be on the left side tucked behind the fairing just below the tank). I used audio wire, because that's all I had then....if you don't like it you can always re-do it with whatever wire you want. Or you can wire it directly to your battery, but I thought I might as well make use of the battery tender connector.