I have noticed that the MQTT third party modules are not available to download if you have selected Ignition 8.1 But they are available for 7.9 and 8.0 Which version of Ignition is recommended when using the MQTT third party module?
You should be able to use the MQTT modules with recent versions of Ignition (including the latest as-of-writing, 8.1.14). See this link for downloads of their 4.0.10 versions:
Note that Cirrus Link have their own testing regimen that they perform against their modules before they certify a given version for use with a given Ignition release. For this reason, there may be some buffer time between a new Ignition release and modules showing up for that release on the Strategic Partner Modules page.
Here is a link to Cirrus Link’s Ignition Version Compatibility documentation as another helpful reference.