$33 later, there was the mighty Ecoworthy.

https://www.amazon.com/dp/B01IFJ73X4

To save money, it was just connected to an LM1117 to limit the voltage to 14.5.  That has a 1V drop at low current & 1.5mA quiescent current.  

Lacking a dummy load, it was easiest to time the charging of a capacitor.  It took around 20 seconds to charge a 36000uF cap to 14.5V in a shaded area.

According to LT, it might have been making 5-10mA in the shade at 13V.  There's a brief time every day when the windshield has direct sunlight.  That's when most of the charging would happen.

 In sunlight, it made 1.5A at 1.5V & the cap charged instantly.  Its peak efficiency is at 18V, so an ideal charger would charge a cap to 18V & discharge just enough current to keep it at 18V.  

A simple PETG enclosure followed.

Then some TPU bumpers would keep it from scratching the car.  A simple trucker's hitch lashed the bumpers down.

Some worthless socks propped it up.  The bumpers definitely made it look more upmarketed than the standard solar panels we see in parking lots.

Helas, in the shaded windshield, it only made 13V with 1.5mA load.   It might be dirt on the windshield, less indirect light under the roof, the load, the panel being rated for lower voltage.  The battery was stuck at its starting voltage of 12.7, whether the panel was fully sunlit or in the shade.  The smaller panel must have generated under 1mA in the shade.

There is no direct sunlight in the summer.  The sun is too high.  Maybe current logging would give more data, but it's a lot of work for what it is.  The lion kingdom doesn't have any other budget besides a $33 panel & linear regulator.  It's easier just to wait another 2 months.