A multimeter is a very useful tool for fault-finding. There’s no need to buy an expensive one (or even one at all if you fancy making your own tester with a buzzer or bulb). With the point in one position and switch installed, there should be a continuous circuit between the matching stock rail and frog. This will show as zero ohms on your multimeter (or a buzzer or light with your home-made tester). From the frog to the opposite stock rail, there should be an open circuit on your meter (no buzzer or light). If there is, then there’s a short somewhere. If all is well, switch the point and test from the other stock rail.