Your readings appear to be consistent with an SSR that is not turning on, so
@Bobby_M 's advice to look at the input voltage on the SSR control inputs (terminals 3 & 4) is a good place to start. The SSR should turn on if the control input voltage is greater than 3V (DC), even tho the nominal voltage for most PID control outputs is ~12V. If the light on the SSR comes on, that just means that the SSR is receiving an adequate control input. It does not mean that the SSR is actually working, as the TRIAC, which is the actual power switch, is electrically isolated from the control input (they are optically coupled.) If the TRIAC, or it's triggering circuit in the SSR, has failed, the light on the SSR will still come on when a valid control voltage is applied.
If you want to test the SSR independently of the PID, you can disconnect the wires from SSR terminals 3 & 4, and connect a nine volt battery (make sure you get the polarity right) to terminals 3 & 4, which should turn the SSR on unless it has failed. With this test you should measure ~240 volts across L1 & L2 at the element (partially plugged in.)
Brew on