Was trying to emulate your problem but realised, mosquitto_pub is not a persistent service. It simply posts a message then dies, so you will not see it in ps aux.
The way you might need to do it is to use cron or similar to call your SH file regularly.
I actually got it working. I had help from another member on the Gitter chat.
I had to set up the service as User=pi in [Service], and then make sure that the code was correct (which is what my biggest problem was). I missed one 0 in my command and it wouldn’t correctly show up.