How did you determine that the ac
system has a full charge?
You did not mention the high pressure reading, so I expect that means you don't have an ac
manifold gauge set.
If the system was empty, and you installed the contents of two 12oz cans, how could the system be full, if the stated capacity is 32ozs?
If you read the pressure with one of those cheap little gauges they come attached to cans of R134a, I hate to burst your bubble, but you still have no idea of what the pressure on the low side is, because the cheap can gauges are horribly inaccurate.
While the low pressure switches located on the accumulator do go bad, they usually will not close the switch to allow the ac
clutch to engage. I have never seen one that would cause the ac
compressor to cycle on and off. For instance, when I bought my 96 Taurus Wagon back in 2001 with 103K miles, the AC
system was not working. After determining that the refrigerant level was low, I added refrigerant, but the ac
clutch would not engine. Even after bringing the refrigerant level up, the ac
clutch still would not engage. Jumping the low pressure switch allowed the ac
clutch to engage, and the system to work. Replacing the the low pressure switch fixed the problem permanently.
Most probably the refrigerant level is still too low (the cause for most ac
system cycling problems). The low pressure switch is working, since the ac
clutch does engage.