I don’t have the electronics background to give you a definitive answer, but I’m not surprised the ring does not light up given the SSR is rated for 25A at 265V. The load is just too light. Unless you are using the SSR for PWM, I suggest a simple, inexpensive mechanical relay module.
Many are rated for 100,000 electrical cycles, and there is no minimum current.
If it must be an SSR, then one of the 2A SSR modules should do the job even with the light load.