Problem driving a 12V/20mA frequency inverter with BC517 transistor

Try connecting terminal 20 to Q1 emitter, Q1 collector to RUN (28?) Arduino output pin to R1 and Arduino GND to 39, should work.

I think I would have to agree.

outsider:
My post should have been:
Try connecting terminal 20 to Q1 emitter, Q1 collector to RUN (28?) Arduino output pin to R1 and Arduino GND to 39, should work.
Switch terminals 20 & 28 in that last picture you posted. Sorry for my confusion. :-[

My bad, because Tom had already corrected that but I didn't know with a PNP current flows from emitter to collector... Thanks for spotting the mistake!
Corrected circuit:

For reference, PNP BC557 connections: (Q1)

NPN BC547: (Q2)