Your testing method is flawed. You shouldn't be using the test light as your ground.
Using the diagram Dads50 posted, connect a jumper wire from the positive of the battery to the center post of the relay. (battery terminal) Use another jumper with your test light from battery - to the 'horn' terminal. This is easier if you have jumpers with clips. Now connect another jumper to battery -. When this last jumper is touched to the 'switch' terminal it should ground the coil, causing the click. This will apply power to the horn terminal and your test lamp will light.
