Wiring the Mean Well RT 125D
You have no load connected, and the data sheet you cited shows minimum loads for each rail (2A for 5V, 0.4A for +24V, 0.1A for 12V).

Not all power supplies can operate at zero load. Operating the power supply outside of specification (i.e. less than the specified current range) isn't guaranteed by the datasheet. Most likely it's losing regulation and shutting down to protect itself.

Try connecting some load and try again. If you have the minimum load on all 3 outputs and the unit still hiccups on and off, it may be defective.