bright stationary star dims and brightens several times

I stepped outside late Tuesday night to admire the extra clear covid-19 lockdown skies.  I found it odd that the south sky had more bright stars than normal.  I traced the curve of the big dipper's handle with my eyes arcing down to Arcturus followed by a brighter white 'star' and then finally to Spica.  The center 'star' was  just about halfway between the other two.  I watched the bright 'star' for about 5 seconds. I could see no evidence of motion.  Being a little rusty on the night sky and beginning to doubt I was looking in the right area, I decided to check myself.  I again found the big dipper and followed the curve of the handle to Arcturus.  Now the middle star was gone.  I fixed on the area trying to find it. Soon it returned in the same place.  As I watched, it dimmed and disappeared for a few seconds then again brightened into view having the same brightness as before.  I failed to find any flashing lights that would belong to an aircraft or notice any slight change in position.  The trees were low and I had nothing close enough for reference on movement.  As I moved to get a tree top closer to my line of sight it again faded to nothing.  I stopped and watched carefully looking for flashing lights or for it to reappear.  I kept my eyes on the south sky for several minutes searching for any light that might be aircraft or satellite, but nothing.
The few times it dimmed or brightened it did so over about 1 second and then held that brightness or lack of.
I know this is rather weak as sightings go and it was quite likely a satellite.  However it did seem unusual when it failed to leave the spot where I originally saw it (as best I could tell), and apparently reflected sunlight to me even though it was on the dark side of the Earth (if it was a satellite).
If I didn't mention something it didn't happen (like lost time).