Given this, you were connected to the low side. Sounds like you were using one of those Wal-mart cans with a fill-hose and gauge built-in? If you were on the high side and the compressor kicked in, it should peg the gauge instantly. Also possible to blow the hose or the can. Now before the compressor cycles on, both ports are almost the same thing and you could add some refrigerant until the system pressure equals the can pressure (in normal charging, the low pressure from the compressor suction helps empty the can). But without any numbers on the gauge, you don't know what it's calling "over-filled". Now if your gauge doesn't move but the compressor is cycling, then something is funky.
The gauge set says it's for R-134? It's possible somebody retro-fitted for a different refrigerant. Technically they're all supposed to have different fittings. The standard fitting for R-134 has never changed.
This is the classic symptom of low refrigerant. Pressure is maintained in the low side by liquid refrigerant boiling. When you run out of refrigerant there's no gas coming to keep up with the compressor so pressure drops very fast. With a proper charge, it will take several seconds for the pressure to come up after the compressor turns off.