It does act like a constant current source. Curiously, I had 4 red LEDs in series and each still glows with the same intensity as the one. That's easy to test, look at the one LED at the base of the string when I'm touching the end of the string versus just that one. No brighter/darker.
A test lead causes a glow of only about 1/5th what I get when I hold onto the end of the lead. Clipping the lead onto an adjacent steel fence pole seems to have the same intensity as me holding it.
I brought my Fluke meter out there, I'm concerned about meter impedance but this is still 60Hz. Curiously, between 2 fence posts- which lit my LEDs equally well as holding onto it- measured nothing on the AC scale. Like 30mV. However, simply holding onto the end measures 60V!!! Wow, I could light up quite a few LEDs this way.
I tried to take a current measurement, but I put it on AC amps and used the 300mA input and got "0.03". The meter reads "0.05" just sitting on the kitchen table so that's not saying much. Say, I should know this, but there's a 300mA and a 10A input here but only one AC and one DC current selection on the dial. How does it "know" which one the desired signal is connected to? If I'm in the "300mA" scale, a reading of "0.03" is 30mA, not 0.03mA, right? Is it just using a single shunt and there's a 300mA fuse instead of the 10A fuse in case you feel the need to protect your circuit from you accidentally shorting it out with a 10A fuse on a current meter? I opened it up and the 10A trace runs past the 300mA trace without joining where I could still see it anyways.