According to Catholicism, what was the basis on which traditional teachings determined the sides on which the Good Thief and the Bad Thief hang?
The Church’s tradition on this subject matter is most likely taken from the fact the left in Latin is sinister, but in English it has a more morbid meaning.
Sinister, today meaning evil or malevolent in some way, comes from a Latin word simply meaning "on the left side." "Left" being associated with evil likely comes from a majority of the population being right handed, biblical texts describing God saving those on the right on Judgment day, and images depicting Eve on Adam's left. Consequently, the Latin for "right," dexter, finds its way into positive words like dexterous, and the French word for right (droit) is found in adroit. - The Left Hand of (Supposed) Darkness
Besides the left side having a traditional sinister meaning, the Bad Thief was hung on the left side of Jesus according to some apocryphal sources as well as the Golden Legend.
In apocryphal writings, the impenitent thief is given the name Gestas, which first appears in the Gospel of Nicodemus, while his companion is called Dismas. Christian tradition holds that Gestas was on the cross to the left of Jesus and Dismas was on the cross to the right of Jesus. In Jacobus de Voragine's Golden Legend, the name of the impenitent thief is given as Gesmas. The impenitent thief is sometimes referred to as the "bad thief" in contrast to the good thief.
The apocryphal Arabic Infancy Gospel refers to Gestas and Dismas as Dumachus and Titus, respectively. According to tradition – seen, for instance, in Henry Wadsworth Longfellow's The Golden Legend – Dumachus was one of a band of robbers who attacked Saint Joseph and the Holy Family on their flight into Egypt. - Impenitent Thief
According to tradition, the Good Thief was crucified to Jesus' right and the other thief was crucified to his left. For this reason, depictions of the crucifixion of Jesus often show Jesus' head inclined to his right, showing his acceptance of the Good Thief. In the Russian Orthodox Church, both crucifixes and crosses are usually made with three bars: the top one, representing the titulus (the inscription that Pontius Pilate wrote and was nailed above Jesus' head); the longer crossbar on which Jesus' hands were nailed; and a slanted bar at the bottom representing the footrest to which Jesus' feet were nailed. The footrest is slanted, pointing up towards the Good Thief, and pointing down towards the other. - Penitent Thief