The problem is that the trigger circuit requires some voltage to operate. It's not the same as a relay contact.
simulate this circuit – Schematic created using CircuitLab
Figure 1. A regular "random" SSR will most likely be constructed similarly to this.
- Most accept a control signal of 3 - 30 V DC. That means that some sort of current limiting circuit is employed to keep the LED current at a safe level.
- D1 and TRI1 will most likely use a ready-made opto-isolator package such as the MOC series. This photo-triac has a low current rating but more than enough to switch on TRI2.
- TRI2 is switched by TRI1 with R1 limiting the current and R2 holding the gate low when TRI1 is off.
- Good SSRs will employ an internal snubber, R3 and C1.
The minimum load mentioned in the comments is related to keeping it on once triggered so that's not your problem.
ASO241 or ASO241R (zero-cross)? This will make a difference too as the zero-cross circuitry is tricky.
Figure 1. Internals of a zero-cross detection circuit based on the G3MB-202P with 5V input.
- If VL1−L2 is low (above but close to zero) and Q1 is turned on by photo-action from D1 then SCR1 will be triggered. This in turn will pass enough current through R6 to bring TRI1 gate voltage high enough to trigger.
- When voltage exceeds a certain level Q2 will be biased on. The collector voltage will fall and there won’t be enough to turn on SCR1 even if Q1 subsequently turns on.
- The effect is that TRI1 can’t turn on unless it is triggered close to the zero cross.
Source: my writing here.