So I came back to the project today. I have found that the clicking in the relay is still sporadic despite making sure all the connections are secured properly. I googled clicking of the relay and I found articles saying there is not enough output voltage to sustain the load. I am using a 12V 2A power source from the wall socket so there shouldn't be any issue there.

To me, your details point to a too low rated supply, in spite of what they claim, the motor is most likely drawing more than the 1a they claim!
Motor circuits are very demanding when on LV, low current supplies.

 

Max is indeed "spot-ON" correct, although the same result can also be caused by a poor connection that duplicates the effect of an inadequate power source. I once solved a problem like that just by turning the Allen screw in a connection lug one turn. It was a 480 volt, three phase motor driving an impressive hydraulic pump. Yes, I did use a well insulated pliers to hold the Allen wrench. AND I was wearing my safety glasses. And that solved the problem.