The real time clock data are accessible to TBASIC as variables:
DATE[1]: Year
DATE[2]: Month
DATE[3]: Date
DATE[4]: Day of the Week.
TIME[1]: hour
TIME[2]: minute
TIME[3]: second
What you need to do is to monitor the real time clock periodically. Since you are only triggering your output once a week, you can check it very irregularly e.g. once a minute. So you can use the 1 minute clock pulse "CLK:1min" to trigger your custom function and you can check the variable to see if it match your criteria. E.g. if every Monday, that means DATE[4] = 1 and at 12:00pm that means TIME[1]=12 and TIME[2]=0 and you will trigger the output. The custom function will be called every 1 minute and only when the DATE[1] and TIME[1] and TIME[2] match the condition would the output be turned ON. You can do the same to turn OFF the output.