I don't understand how can I get the Developer License for my JIRA test environment.
In the documentation the following is written:
But there's no View Developer License' link in the bottom right corner of the license detail panel, below my commercial license key.
You are correct on this, as you cannot do this.
Only one instance is allowed to run live for one license. You may purchase two 100 Users license and have them for each of your JIRA instances.
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