it sounds like you have a leak in the locking circuit. you may have others.
Can you run the engine for a few minutes with the doors locked and then shut the car off. Then wait a few minutes. Try to unlock the doors either with the key from the outside or from inside the car with the lock button.

What does that do?
Try the same thing with running the car and then shutting it off and try to lock the doors.

What is that result?

Without a vacuum pump, it will be harder, but you can diagnose and repair the system without one. It will just take longer.

Try the above and post what you find.
Note the speed at which the doors lock and unlock.
Is one or more door faster to respond than the others?

Check it out and post what you find