Disk Utility is not showing me an obvious place to find an option to Secure Erase (zero out) an external hard drive.
I was able to zero an external drive. And since erasing an external drive was your stated goal, why didn't you select an external drive instead of your internal Apple SSD?


And Disk Utility is not going to knowingly erase the boot drive, which it appears you have selected for you screen shot.
And it turns out disk drives and SSDs make it extremely difficult to perform a true guaranteed secure erase, as the rotating devices perform sector replacement where knowledgeable individuals can recover data from it after a secure erase, and SSDs never write to the sector where the data is stored, then always write to a new sector, and must move the original sector to a garbage collection area, where again knowledgeable individuals can recover your data. As a result it is not wise to declare something 'secure' when it isn't.
Finally, writing zeros on an SSD, besides not actually zeroing what you think you are zeroing (as in it can leave a few gigabytes of your original data still accessible), the zeroing also shortens the life of the SSD. SSDs have a limited number of writes per sector before the material physically wears out. The SSD does wear leveling to help avoid this, but zeroing an entire SSD (or worse 7 or 35 pass random patterns), can seriously reduce the life of the SSD.
With SSDs, it is better to operate them full time as FileVault encrypted drives and then as Barney-15E suggests, just do a reformat which will throw away the old encryption key and then sectors will just be a bunch of random bits. No need to write any zeros and shorten the life of the SSD.