Your references will be asked about your attitude on the slow Tuesday shifts. Give them something good to say.

What gets reported about you is your behaviour when nothing much was happening. Anybody looks good during a rush, so whoever is asked about you reaches for the ordinary stretches: were you on your phone, did you find something useful, were you decent to the one customer who came in. That is where character is visible, because there is nothing else to look at. The quiet hours are the ones being remembered.

So treat the empty part of a shift as the actual test. Clean something, learn something, talk properly to whoever is there. It costs you a dull hour and it buys the sentence somebody says about you later.