If those checks don’t show anything up can you post the full output of the Mosquitto service status and also the service log using
sudo journalctl -u mosquitto
plus this command
ls -la /etc/Mosquitto
so we can see the file ownership and permissions etc.
Assuming the password is the same, it looks a lot like the old Mosquitto starting issues that led to delays being added to rc.local, have you run the emonpiupdater since creating the image? Can you show us the contents of /etc/rc.local?
(See the Mosquitto not starting after emonSD update & upgrade and Mosquitto won't start on boot after raspbian and emonsd update and MQTT Log files threads)
There is also the version of Mosquitto you have installed to consider, as far as I know, 1.5 hasn’t been tested with the OEM stuff yet. The emonSD image only had 1.4.10 installed and even now Glyn is trialing a emonSD that is upgraded from jessie to Stretch (not a fresh install) that also uses 1.4.10. Versions 1.4.14 and 1.4.15 have made appearances on the forum, but not necessarily on an emonSD image. I think @borpin has tried 1.4.15 and is now running 1.4.14 on a DietPi image, so you are straying off the beaten path a little with 1.5.
[edit] I have just seen your post and you have found the log issue, I will post this anyway as the linked threads explain the issues you may face depending on how or more importantly when you create the Mosquitto log file. The delays in rc.local are essential.
[edit2] the changes to rc.local are in the “low-write mode emoncms optimisations” of the emonSD build guide and there is a new rc.local file included in the repo (emonpi/rc.local_jessieminimal at master · openenergymonitor/emonpi · GitHub) although there is also this in the emoncms/scripts/logger repo too (emoncms/scripts/logger at master · emoncms/emoncms · GitHub).