If by Timer script, you mean install OnTimer, this runs on a given FileMaker window for as long as the window is open--so you'd have to keep the window open 24/7 in order for that to work. Thus it's best suited for controlling the time of day that a script executes or to run the same script repeatedly with a specified interval in seconds between each call to the second script.
There are other options for running a script on a monthly schedule that do not have this limitation. You can use Scheduler in FileMaker server to run the script on a daily basis and the script can exit without doing anything except when the date is the first day (or any specified day) of the month.
In similar fashion Windows Task Manager (there are mac equivalents, I am told) can be used to open a Filemaker file. A script in this file can run when the file is opened that checks the date just like I described in the previous option and runs the second script if the specified day of the month matches the day of the current date. This can be a small "robot" file that performs scripts in your main file and avoids limitations that you can encounter when using Server's scheduler to run the script.