The car may or may not be related to the crime. But, there are certainly some possible answers to address the questions you pose.
Why waste time driving around SWFA? Why, indeed. If we try to keep this simple and not overthink it, here is what I come up with. If I see a car pull into a business, turn its lights off and back on a few times, and drive slowly around the perimeter, isn’t it most likely that the driver is there because there is something interesting about that business? And doesn’t the headlight flashing and perimeter drive make it pretty unlikely that the driver is just taking a break?
As far as outing the vehicle, that hasn’t happened in 5 years. Police still don’t know how it is. To me that makes it likely that the driver switched license plates.
The potential answer that makes the best sense to me is that the killer did pull into SWFA before ever setting foot at the church. In fact, SWFA may have been a target they were considering either to hit that night or in the future. Turning off the headlights allows the driver to see into the building better, without reflection glare. They then drive around in order to assess points of entry and exit. And when they come back around and park, they are directly facing the entrance and can sit there taking notes.
So upon leaving the SWFA, SP either notices the church and decides to check it out, or else they were already considering it as their Plan B. Either way, they find it the best option for that night, and they do some things to test for a police response. Once that is done, they go back and enter the church.