A/C Clutch not cycling ie turning off

Working from a vague memory here and it's been a while so bare with me:

There's a box behind the passenger side dash that contains the thermal switch (up against the plastic face between the vents). Some (I think) have an adjustment dial while others did not (depending on year). If yours has an adjustment dial, give that a shot first. You should be able to set the tempurature cut-off threshold with that dial. If there's no dial then you may need to break that little box open to inspect/clean the contacts. Short of that, the box may require replacement.

Prior to opening the box though... you should be able to manually open and close that circuit with a metal clip or wire to ensure the circuit is working.

Based on your description? No. If your system was low on pressure then the clutch would not engage at all.