Hello and welcome here
The pcb you show have rectifier and regulator, so the input is AC
anode is positive, the silkscreen seem to show it on the left, as you assume
I don't remember well but I think it's connected to a pic output, so should show some activity.
Have a search, @TK. work on a wireless PIC replacement for this board , also @Antichambre have a super small STM32 board with PIC pinout compatibility IIRC
should not be that complicated (for those who know how to) to make this MIOS8 app running on MIOS32
Best
Zam