I’m not an adept automation designer, but if this is really of value for a specific use cases and hence worth the effort, could this not be solved by scheduling a weekly activity that triggers a simple automation that verifies whether or not it is the first Tuesday of the month / alternatively if it’s the fourth time that it was called upon, which then triggers the actual action that you want to perform each first Tuesday of the month / each 4th Tuesday, if the condition is true?

Seems to me like the additional scripting would be fairly limited.  E.g. for each 4th run you would have an automation that increments a counter (stored in a persistent memory to survive system reboots), and if it hits 4 you reset it to start all over and also trigger the desired procedure.  And you set the scheduler to run each Tuesday, but the desired procedure would only effectively run each 4th Tuesday.  It could probably be made quite generically (i.e. an automation that you can probably give a nbr to define the nbr of weeks and the name of the subscript that has to be called upon).

Again, not sure what the use case is, and how valuable it is and hence if it justifies the extra effort.