I noticed that the O.P. has already started a new thread asking about a suitable AC voltage dropping capacitor, but I have a suggestion of my own. Perhaps it's too late, though.
I noticed that Jaycar have a transformer (MM-2002) with multiple output taps (6.3V, 7.5V, 8.5V and others) which could be used to directly drive a red LED (Vf =1.8V) or a pair of anti-parallel red LEDs. Using the 6.3V and 7.5V taps, it's possible to get 1.2V - 1.3V (RMS) which equates to approximately 1.8V peak across the red LED. There's no need for a current limiting resistor since the DC winding resistance between the secondary taps is probably enough. I should mention that the transformer is rated at 15VA which is obviously excessive for driving the LED, but the voltage taps are suitable, though.
Alternatively, it might be possible to use an NCP785A "wide input voltage range linear regulator" to output 3.3VDC to drive an LED up to a few mA. A current limiting resistor would be required to be connected between the output of the linear regulator and the LED.
Link to the Jaycar transformer:
https://www.jaycar.com.au/6-3-15v-15va-1a-multi-tapped-type-2155/p/MM2002Link to the NCP785A datasheet:
https://www.onsemi.com/pdf/datasheet/ncp785a-d.pdfThere's also an EEVBlog discussion thread:
https://www.eevblog.com/forum/blog/eevblog-1285-how-to-do-design-by-inspection