Full time trader is the person who makes living from trading. It has nothing to do with how frequently or how many hours, he trades, . There are many trading styles where traders don't monitor each and evey bar. They can swing trade, they can trade for first 2 hrs of the market, trade for first 1 hr and last 1hr of the market when there is action etc.. and make living from trading.
Every successful daytraders know it well, that when is the time to trade and when is the time to stand on the side (which is almost 75% of the day).
And if one uses the technology correctly, then one can devise the alarm notification system to attract traders attention.
So, why not, if your system is right then you can very well execute one trade on Monday...and make the money for whole week. Better, exeute a trade once in a month.