1) Bought the car...door locks were a little slow to act (after car was shut off)...no big deal...don't lock the doors anyways.
2) 3 months later, car won't shut off...locks won't work at all...unless car is running.
3) 3 months later (now) brake pedal is hard as a rock.

Just putting my finger over the vacuum pump connection shows a good vacuum. So I guess I should move up the line(s) from there.

Is there a good guide somewhere that goes through the appropriate sequence for checking the system components so that I don't miss anything? And is there a vacuum tester that's recommended?

Thanks!

Measure how many inches of vacuum your pump makes by itself.

Mityvac is a good pump/tester

Then you can start diagnosing individual systems:


Central locking / brake booster vacuum diagrams(your model is 123.1):

https://www.startekinfo.com/StarTek/outside/12265/disc_2/program/Chassis/80-901.pdf

https://www.startekinfo.com/StarTek/outside/12265/disc_2/program/Chassis/80-900.pdf

page 3 has a diagram for the shutoff system:

https://www.startekinfo.com/StarTek/outside/12265/disc_2/program/Engine/615/07-150.pdf

Thanks so much Christuna!
And thank you for those diagrams...very helpful indeed!
I'll do my best.