Sure I used the automatic shutter on my ES-II a lot! But now I do everything manually when I can.
Super-Takumar lenses are the ones which require stop-down metering. Yours is not that.
A very tiny pin, the square block and the lever which moves with the aperture... prove 100% compatibility with Spotmatic-F and ES, ES-II.
True, Asahi vs. Honeywell might explain the (cosmetic-only) difference in lens styling. But I just suspected that the previous owner swapped the lens out. A little projecting of my own devious nature here. My Honeywell ES-II has a similar style Asahi Super-Multi-Coated Takumar 50mm f/1.4 mounted to it because I swapped the lens out with my dad. He is stuck with my 50mm f/1.8 rugged knurl lens on his Asahi Spotmatic-II. The Spotmatic-II didn't need the block and lever, but the very tiny pin is there to support the Spotmatic-II.
The lens has a lever that switches between Manual and Auto. That describes the aperture automatically opening only, a confusing term. For the ES-II please make sure that you set that slider on the lens to Auto. The tiny pin is a safety interlock that prevents you from switching it to Manual, Manual is a bad setting for the ES-II. Won't break anything but it will ruin a lot of exposures. If you played with it, set it back to Auto.