I would use the TT560 on the camera. You can do a test in the common area(s) of the already lit area you mentioned by doing some sample shots and checking the results. You can set your camera to Manual mode, something like F9 aperture, 180 shutter speed sync for the flash if it requires it, and ISO 200. You can test with flash by starting at approximately 1/8 power, checking results, and if necessary change the flash power for brighter/dimmer or change the ISO for more brightness if needed. The test shots will tell which settings can be used where, and what settings perform best in most areas. You can view the histogram of your image results to see if they are turning out alright, and also your image, both in your rear lcd screen.
I know you can use TAV if you want to, but Manual camera mode will give you control over ISO use/results. Of course the decision is up to you, but when you get past 1600 ISO for example, most likely you may start to get image noise which you will not have in 200, 400, or 800 ISO images. If you have a flash, you should not have to stray above 400 ISO in most cases. That is the advantage of a flash.
Also, if you want to avoid any of the testing I mentioned, and have automated metering while using a flash (P-TTL), I would recommend a Yongnuo YN585EX flash for Pentax. This type flash will allow you to be in Manual mode on the camera with the settings you
want, and the flash itself will assess the light needed for your subject and emit that amount automatically. Below is a path to the Yongnuo YN585EX for Pentax in case you are interested.
Yongnuo YN585EX Speedlite for Pentax Cameras YN585EX/PENTAX B&H