I won't bother with the displacement feud as I started on a liter bike, and reluctantly admitted it was too much bike after my first low-side; so despite having track experience on turbo cars, I couldn't adapt to the hp. I went down to 600 as it was a good deal on a pro-am race bike.
My race bike (in the avatar) developed a leak that took me forever to find after storing it after my last track day late 2017; at first I thought it was my Ohlins cartridges, but then ruled it out after stripping the fairings. Then I thought it was the oil pan as it looked like oil diluted with some fluid. Then thought it was the stator cover etc... this went on over the off-season.
Long short after going over everything with fluid I found it was a cheap Chinese petcock on my tank dripping gas and mixing with some residual debris/tire/oil on the chassis. This took months to pinpoint as it was the most unlikely culprit considering how much money was spent on the parts suspension/rear sets/clip-ons/quick shift etc... I only found out what it was yesterday after a really hard shake down and stripping the tail/belly pan.
Ask to have the fairings (at least belly pan) taken off and have it up in the air with a rear jack and take it through all the gears on cold start up and have a look over after getting in warm. This assumes it has rear sliders, of course, but what race bike doesn't have any?
In my experience, most won't let you test ride unless you have cash on hand and are super eager to sell it as they aren't usually road legal, so getting a feel for how she runs is critical. Just know that a race bike has been abused, regardless, so some wrenching and replacement of parts on your end will be required.