pajero v6 3500 gdi

would anyone have an idea on how fast the temp of the catalytic converter shoots up from cold? im having this problem with the CAT light on the dash, most times it lights up just after 5mins of driving from cold, the temp gauge hasnt even reached middle yet. and then eventually the light will go off. there are times when i hit an uphill slope, the light would come on right away but when im on descent it turns off. there was this time i was on a flat surface and the light turned on, i tried revving the car upto 5k rpm and the light shut off. (but this doesnt alwasy work) so now im thinking it might be a wiring problem, when the light was on i went under the car and played with the connectors and wires of the sensor to no success, i thought that if it was a loose connection, i could jiggle it and the light will turn off.

just this morning when i started the car, the light was already on. didnt use the car today. so i dont know if it will shut off eventually.

should i be alarmed? at first i thought that i just put in a bad fuel additive and mucked it up. but now being the light was on when i started the car, im thinking it might be a loose connection or the sensor itself

any help will be greatly appreciated